这

T H E

物理学的演化

E V O L U T I O N O F P H Y S I C S

物理学的演化

T H E E V O L U T I O N O F P H Y S IC S

作者：A.爱因斯坦和L.英菲尔德

B Y A. E I N S T E I N A N D L. I N F E L D

首次出现在

first appeared in

剑桥图书馆

T H E C A M B R I D G E L I B R A R Y

现代科学,

O F M O D E R N S C I E N C E ,

一系列新书描述了

a series of new books describing, in

语言适合一般非专业读者，目前 在现代科学的许多分支领域中的地位。

language suitable for the general nonspecialist reader, the present position in many branches of modern science.

本系列由 D r C . P. Snow 编辑， 由

The series is edited by D r C . P. Snow, and is published by

剑桥大学出版社

C A M B R I D G E U N I V E R S I T Y P R E S S

尤斯顿路本特利豪斯

B E N T L E Y H O U S E , E U S T O N R O A D

伦敦，西北一区

L O N D O N , N . W . I

演变

T H E E V O L U T I O N OF

物理

P H Y S IC S

经过

阿尔伯特·斯坦

A L B E R T E I N S T E I N

利奥波尔丁菲尔德

L E O P O L D I N F E L D

科学图书俱乐部

T H E S C I E N T I F I C B O O K C L U B

查令十字路 111 号

111 C H A R I N G C R O S S R O A D

伦敦 WC 3

L O N D O N W.C. 3

前言

P R E F A C E

在开始阅读之前，你当然希望一些简单的问题得到解答。这本书是为了什么目的而写的？这本书的假想读者是谁？

B e f o r e you begin reading, you rightly expect some simple questions to be answered. For what purpose has this book been written? Who is the imaginary reader for whom it is meant?

一开始就清楚而令人信服地回答这些问题是困难的。如果在书的最后再回答，那就容易多了，尽管这完全是多余的。我们发现，更简单的方法是说出这本书不打算成为什么。我们写的不是一本物理学教科书。本书不是关于基本物理事实和理论的系统课程。我们的目的是概括地勾勒出人类思维试图在思想世界和现象世界之间寻找联系的尝试。我们试图展示迫使科学发明与我们世界的现实相符的思想的积极力量。但我们的表述必须简单。在事实和概念的迷宫中，我们必须选择一条我们认为最具特色和意义的道路。

It is difficult to begin by answering these questions clearly and convincingly. This would be much easier, though quite superfluous, at the end of the book. We find it simpler to say just what this book does not intend to be. We have not written a textbook of physics. Here is no systematic course in elementary physical facts and theories. O ur intention was rather to sketch in broad outline the attempts o f the human mind to find a connection between the world of ideas and the world o f phenomena. We have tried to show the active forces which compel science to invent ideas corresponding to the reality o f our world. But our representation had to be simple. Through the maze of facts and concepts we had to choose some highway which seemed to us most characteristic and significant.

这条路没有触及的事实和理论必须被省略。我们的总体目标迫使我们做出明确的事实和想法选择。问题的重要性不应根据其篇幅来判断。一些重要的思路被省略了，不是因为它们在我们看来不重要，而是因为它们不在我们选择的路上。

Facts and theories not reached by this road had to be omitted. We were forced, by our general aim, to make a definite choice of facts and ideas. The importance of a problem should not be judged by the number o f pages devoted to it. Some essential lines of thought have been left out, not because they seemed to us unimportant, but because they do not lie along the road we have chosen.

六

在写这本书时，我们花了很长时间讨论我们理想读者的特点，并对他非常担心。我们希望他能用许多优点来弥补物理和数学具体知识的完全缺乏。

Whilst writing the book we had long discussions as to the characteristics of our idealized reader and worried a good deal about him. We had him making up for a complete lack of any concrete knowledge of physics and mathematics by quite a great number of virtues.

我们发现他对物理和哲学思想很感兴趣，我们不得不佩服他为阅读那些不太有趣和较难的段落所付出的耐心。他意识到，为了理解任何一页，他必须仔细阅读前面的内容。他知道，一本科学书籍，即使很受欢迎，也不能像读小说一样去阅读。

We found him interested in physical and philosophical ideas and we were forced to admire the patience with which he struggled through the less interesting and more difficult passages. H e realized that in order to understand any page he must have read the preceding ones carefully. H e knew that a scientific book, even though popular, must not be read in the same way as a novel.

这本书只是我们和你之间的一次简单聊天。你可能会觉得它无聊或有趣，枯燥或令人兴奋，但如果这些内容能让你了解人类富有创造力的头脑为更全面地理解物理现象的规律而进行的永恒斗争，那么我们的目的就达到了。

The book is a simple chat between you and us. You may find it boring or interesting, dull or exciting, but our aim will be accomplished if these pages give you some idea o f the eternal struggle of the inventive human mind for a fuller understanding of the laws governing physical phenomena.

声发射

A. E.

李

L. I.

致谢

A C K N O W L E D G M E N T S

我们要感谢所有在本书编写过程中给予我们帮助的人，特别是：新泽西州普林斯顿的 A. G. Shenstone 教授和波兰利沃夫的圣洛里亚教授，他们为本书提供了第 III 版的照片。

W e w ish to thank all those who have so kindly helped us with the preparation of this book, in particular: Professors A . G . Shenstone, Princeton, N .J ., and St Loria, Lwow, Poland, for photographs on plate I I I .

I. N. Steinberg 的绘画作品。

I. N . Steinberg for his drawings.

D r M . Phillips 阅读手稿并给予大力帮助。

D r M . Phillips for reading the manuscript and for her very kind help.

声发射

A. E.

李

L. I.

内容

C O N T E N T S

一、存在机械观点

I. T H E R IS E O F T H E M E C H A N I C A L V I E W

伟大的神秘故事

The great mystery story

第 3页

page 3

第一个线索

The first clue

向量

Vectors

运动之谜

The riddle of motion

一条线索

O ne clue remains

三十四

热是物质吗？

Is heat a substance?

三十八

逆转

The switchback

四十七

汇率

The rate o f exchange

哲学背景

The philosophical background

物质动能论

The kinetic theory o f matter

二.

II.

机械观的衰落

T H E D E C L I N E O F T H E M E C H A N I C A L V IE W

两种电流体

The two electric fluids

磁性流体

The magnetic fluids

第一个严重的困难

The first serious difficulty

光速

The velocity o f light

光作为物质

Light as substance

颜色之谜

The riddle of colour

100

什么是波？

What is a wave?

104

光的波动说

The wave theory of light

110

纵向光波还是横向光波？

Longitudinal or transverse light waves?

120

以太与机械观

Ether and the mechanical view

123

三

III.

. 相对论场 ;

F I E L D , R E L A T I V I T Y

场作为表征

The field as representation

129

场论的两大支柱

The two pillars of the field theory

142

十

该领域的现实

T he reality o f the field

第 148页

page 148

场与以太

Field and ether

156

机械脚手架

T he mechanical scaffold

160

以太与运动

Ether and motion

172

时间、距离、相对论

T im e, distance, relativity

186

相对论和力学

Relativity and mechanics

202

时空连续体

T he time-space continuum

209

广义相对论

General relativity

220

电梯内外

Outside and inside the lift

226

几何与实验

Geometry and experiment

235

广义相对论及其验证

General relativity and its verification

249

场与物质

Field and matter

255

四、量子

IV . Q U A N T A

连续性、不连续性

Continuity, discontinuity

263

物质的基本量子和电 265

Elementary quanta o f matter and electricity 265

光的量子

T he quanta o f light

272

光谱

Light spectra

280

物质波

T he waves o f matter

286

概率波

Probability waves

294

物理与现实

Physics and reality

310

指数

Index

3 17

车牌清单

L I S T O F P L A T E S

图 1. 布朗运动

Plate 1. Brownian movement

面对第 66页

facing page 66

光的衍射

II. Diffraction o f light

118

III. X射线和电子波的谱线、衍射

III. Spectral lines, diffraction o f X-rays and of electronic waves

286

一、崛起

I. THE RISE

机械观

OF THE MECHANICAL VIEW

忒瑞斯

T H E R I S E

机械观

OF T H E M E C H A N I C A L V I E W

伟大的神秘故事——第一条线索—— 矢量——运动之谜 ——仅剩一条线索——热是一种物质吗？—— 折返——汇率——哲学背景——物质的动力学理论 伟大的神秘故事

The great mystery story— The first clue— Vectors— The riddle o f motion— One clue remains—Is heat a substance?— The switchback— The rate o f exchange— The philosophical background— The kinetic theory o f matter T H E G R E A T M Y S T E R Y S T O R Y

在想象中 存在着完美的神秘故事。

I n im agin a tio n there exists the perfect mystery story.

这样的故事提供了所有必要的线索，迫使我们形成自己的案件理论。如果我们仔细跟随情节，我们会在书的结尾作者披露之前找到完整的解决方案。与那些低级神秘故事相反，解决方案本身并没有让我们失望；而且，它出现在我们期待的那一刻。

Such a story presents all the essential clues, and compels us to form our own theory o f the case. I f we follow the plot carefully, we arrive at the complete solution for ourselves just before the author’s disclosure at the end of the book. The solution itself, contrary to those of inferior mysteries, does not disappoint us; moreover, it appears at the very moment we expect it.

我们能否将这本书的读者比作一代又一代在自然之书中不断寻求解答的科学家呢？这种比较是错误的，以后必须放弃，但它有一定道理，可以加以扩展和修改，使其更适合科学解决宇宙之谜的努力。

C an we liken the reader of such a book to the scientists, who throughout successive generations continue to seek solutions of the mysteries in the book o f nature? The comparison is false and will have to be abandoned later, but it has a modicum of justification which may be extended and modified to make it more appropriate to the endeavour o f science to solve the mystery of the universe.

这个伟大的谜团至今仍未解开。我们无法

This great mystery story is still unsolved. We cannot

甚至确信它有一个最终的解决方案。阅读已经给了我们很多；它教会了我们自然语言的基本知识；它使我们能够理解许多线索，并且成为科学进步中常常痛苦的快乐和兴奋的源泉。但我们意识到，尽管阅读和理解了这么多卷，我们仍然远未找到一个完整的解决方案，如果确实存在这样的解决方案的话。

even be sure that it has a final solution. The reading has already given us much; it has taught us the rudiments o f the language of nature; it has enabled us to understand many of the clues, and has been a source o f joy and excitement in the oftentimes painful advance o f science. But we realize that in spite of all the volumes read and understood we are still far from a complete solution, if, indeed, such a thing exists at all.

在每个阶段，我们都试图找到与已发现的线索一致的解释。暂时接受的理论已经解释了许多事实，但尚未发展出与所有已知线索兼容的通用解决方案。很多时候，看似完美的理论在进一步阅读后被证明是不充分的。

A t every stage we try to find an explanation consistent with the clues already discovered. Tentatively accepted theories have explained many o f the facts, but no general solution compatible with all known clues has yet been evolved. Very often a seemingly perfect theory has proved inadequate in the light o f further reading.

新的事实出现了，与理论相矛盾或无法用理论解释。我们读得越多，就越能充分体会到这本书的完美构造，尽管随着我们不断前进，完整的解决方案似乎越来越渺茫。

New facts appear, contradicting the theory or unexplained by it. The more we read, the more fully do we appreciate the perfect construction of the book, even though a complete solution seems to recede as we advance.

自柯南·道尔的精彩故事以来，几乎每一部侦探小说都会有这样一个时刻：侦探已经收集了至少在某个阶段需要的所有事实。这些事实往往看起来很奇怪、不连贯、毫无关联。然而，伟大的侦探意识到，此时不需要进一步调查，只有纯粹的思考才能将收集到的事实联系起来。

In nearly every detective novel since the admirable stories o f Conan Doyle there comes a time when the investigator has collected all the facts he needs for at least some phase of his problem. These facts often seem quite strange, incoherent, and wholly unrelated. The great detective, however, realizes that no further investigation is needed at the moment, and that only pure thinking will lead to a correlation of the facts collected.

于是他拉起小提琴，或者躺在扶手椅上抽着烟斗，突然间，天哪，他得到了它！他不仅对手头的线索有了解释，

So he plays his violin, or lounges in his armchair enjoying a pipe, when suddenly, by Jo v e , he has i t ! Not only does he have an explanation for the clues at hand,

但他知道一定发生了其他事件。既然他现在知道该去哪里寻找它，他可以出去，如果他愿意的话，为他的理论收集进一步的证据。

but he knows that certain other events must have happened. Since he now knows exactly where to look for it, he may go out, if he likes, to collect further confirmation for his theory.

如果我们可以重复这句陈词滥调的话，阅读自然之书的科学家必须自己找到答案；因为他不能像其他故事的不耐烦的读者那样，翻到书的结尾。

The scientist reading the book of nature, if we may be allowed to repeat the trite phrase, must find the solution for himself; for he cannot, as impatient readers of other stories often do, turn to the end of the book.

在我们的案例中，读者也是研究者，他们试图至少部分地解释事件与其丰富背景之间的关系。为了获得哪怕是部分解决方案，科学家必须收集可用的无序事实，并通过创造性思维使它们连贯且易于理解。

In our case the reader is also the investigator, seeking to explain, at least in part, the relation o f events to their rich context. To obtain even a partial solution the scientist must collect the unordered facts available and make them coherent and understandable by creative thought.

在接下来的几页中，我们的目标是概括描述物理学家的工作，这些工作与研究人员的纯粹思维相对应。我们将主要关注思想和观念在探索物理世界知识的过程中所起的作用。

It is our aim, in the following pages, to describe in broad outline that work of physicists which corresponds to the pure thinking o f the investigator. We shall be chiefly concerned with the role of thoughts and ideas in the adventurous search for knowledge of the physical world.

线索

T H E F IR S T C L U E

尝试解读这个伟大的神秘故事的历史与人类思想本身一样悠久。然而，直到三百多年前，科学家才开始理解这个故事的语言。从那时起，也就是伽利略和牛顿的时代，解读工作进展迅速。

Attempts to read the great mystery story are as old as human thought itself. O nly a little over three hundred years ago, however, did scientists begin to understand the language of the story. Since that time, the age of Galileo and Newton, the reading has proceeded rapidly.

调查技术、寻找和跟踪线索的系统方法已经发展起来。一些

Techniques of investigation, systematic methods of finding and following clues, have been developed. Some of

大自然的谜题有6

the riddles o f nature have 6

已经解决，尽管许多

been solved, although many

进一步的研究证明，这些解决方案都是暂时的、肤浅的。

o f the solutions have proved temporary and superficial in the light of further research.

一个最基本的问题是运动问题，数千年来，它一直因其复杂性而被完全掩盖。

A most fundamental problem, for thousands of years wholly obscured by its complications, is that o f motion.

我们在自然界中观察到的所有运动——一块石头被抛向空中，一艘船在海上航行，一辆手推车在街道上行驶——实际上都是非常复杂的。

A ll those motions we observe in nature— that o f a stone thrown into the air, a ship sailing the sea, a cart pushed along the street— are in reality very intricate.

要理解这些现象，明智的做法是从最简单的情况开始，然后逐步进展到更复杂的情况。考虑一个静止的物体，根本没有运动。要改变这种物体的位置，必须对它施加某种影响，推它或举它，或者让其他物体（如马或蒸汽机）对它作用。我们的直觉认为，运动与推、举或拉的动作有关。反复的经验会让我们冒险进一步说，如果我们想让物体移动得更快，就必须用更大的力推。似乎很自然地得出结论，对物体施加的作用越大，它的速度就越快。四匹马拉的马车比只有两匹马拉的马车跑得快。

T o understand these phenomena it is wise to begin with the simplest possible cases, and proceed gradually to the more complicated ones. Consider a body at rest, where there is no motion at all. T o change the position o f such a body it is necessary to exert some influence upon it, to push it or lift it, or let other bodies, such as horses or steam engines, act upon it. O ur intuitive idea is that motion is connected with the acts o f pushing, lifting or pulling. Repeated experience would make us risk the further statement that we must push harder if we wish to move the body faster. It seems natural to conclude that the stronger the action exerted on a body, the greater will be its speed. A four-horse carriage goes faster than a carriage drawn by only two horses.

直觉告诉我们，速度本质上与行动相关。

Intuition thus tells us that speed is essentially connected with action.

侦探小说的读者都知道，错误的线索会使故事混乱，并推迟解决问题。直觉所决定的推理方法是错误的，并导致了几个世纪以来错误的运动观念。亚里士多德在整个欧洲的伟大权威也许是导致

It is a familiar fact to readers of detective fiction that a false clue muddles the story and postpones the solution. The method o f reasoning dictated by intuition was wrong and led to false ideas o f motion which were held for centuries. Aristotle’s great authority throughout Europe was perhaps the chief reason for

长期以来，人们一直相信这一直观的想法。我们在两千年来一直归于他的《力学》中读到：当推动物体前进的力不再起到推动物体的作用时，运动物体就会停止。

the long belief in this intuitive idea. We read in the Mechanics, for two thousand years attributed to him: The moving body comes to a standstill when the force which pushes it along can no longer so act as to push it.

伽利略发现并运用科学推理是人类思想史上最重要的成就之一，标志着物理学的真正开端。这一发现告诉我们，基于直接观察的直觉结论并不总是可靠的，因为它们有时会带来错误的线索。

The discovery and use o f scientific reasoning by Galileo was one of the most important achievements in the history o f human thought, and marks the real beginning of physics. This discovery taught us that intuitive conclusions based on immediate observation are not always to be trusted, for they sometimes lead to the wrong clues.

但直觉哪里错了？说四匹马拉的马车一定比两匹马拉的马车跑得快，这难道会错吗？

But where does intuition go wrong? C an it possibly be wrong to say that a carriage drawn by four horses must travel faster than one drawn by only two?

让我们更仔细地研究运动的基本事实，从人类自文明开始以来所熟悉的、在艰苦的生存斗争中获得的简单的日常经验开始。

Let us examine the fundamental facts o f motion more closely, starting with simple everyday experiences familiar to mankind since the beginning o f civilization and gained in the hard struggle for existence.

假设有人推着手推车沿着平坦的道路行驶，突然停止推车。手推车会继续行驶一小段距离，然后停下来。

Suppose that someone going along a level road with a pushcart suddenly stops pushing. The cart will go on moving for a short distance before coming to rest.

我们不禁要问：怎样才能增加这个距离呢？

We ask: how is it possible to increase this distance?

有很多方法，比如给车轮上油，把路面修得非常平整。车轮转动得越容易，路面越平整，车子就能行驶得越久。上油和修平究竟起了什么作用呢？只有一点：外部影响变小了。所谓的摩擦力的影响已经减弱，无论是在车轮中还是在车轮和路面之间。这是

There are various ways, such as oiling the wheels, and making the road very smooth. The more easily the wheels turn, and the smoother the road, the longer the cart will go on moving. A nd just what has been done by the oiling and smoothing? O nly this: the external influences have been made smaller. The effect o f what is called friction has been diminished, both in the wheels and between the wheels and the road. This is

这已经是对可观察证据的理论解释，事实上，这种解释是任意的。

already a theoretical interpretation o f the observable evidence, an interpretation which is, in fact, arbitrary.

再向前迈出重要一步，我们就会找到正确的线索。想象一条道路非常平坦，车轮没有一点摩擦力。那么就没有什么可以阻止这辆车，这样它就可以永远行驶下去。这个结论只能通过想象一个理想化的实验来得出，而这个实验永远不可能真正进行，因为不可能消除所有外部影响。

O ne significant step farther and we shall have the right clue. Imagine a road perfectly smooth, and wheels with no friction at all. Then there would be nothing to stop the cart, so that it would run for ever. This conclusion is reached only by thinking o f an idealized experiment, which can never be actually performed, since it is impossible to eliminate all external influences.

理想化的实验揭示了真正构成运动力学基础的线索。

The idealized experiment shows the clue which really formed the foundation of the mechanics o f motion.

比较两种解决问题的方法，我们可以说：直观的想法是——作用越大，速度越大。因此速度表明外力是否作用于物体。伽利略发现的新线索是：如果物体既没有被推、拉，也没有以任何其他方式受到作用，或者更简单地说，如果没有外力作用于物体，那么它会匀速运动，即始终以相同的速度沿直线运动。因此速度并不能表明外力是否作用于物体。伽利略的结论是正确的，一代人之后，牛顿将其表述为惯性定律。它通常是我们在学校里背诵的第一件物理学知识，我们中的一些人可能还记得它：

Comparing the two methods of approaching the problem, we can say: the intuitive idea is— the greater the action, the greater the velocity. Thus the velocity shows whether or not external forces are acting on a body. The new clue found by Galileo is: if a body is neither pushed, pulled, nor acted on in any other way, or, more briefly, if no external forces act on a body, it moves uniformly, that is, always with the same velocity along a straight line. Thus, the velocity does not show whether or not external forces are acting on a body. Galileo’s conclusion, the correct one, was formulated a generation later by Newton as the law o f inertia. It is usually the first thing about physics which we learn by heart in school, and some o f us may remember it:

任何物体都会保持其静止状态或沿直线的匀速运动状态，除非受到施加在其上的力而被迫改变该状态。

Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.

我们已经看到，这个惯性定律不能

We have seen that this law of inertia cannot be

直接来自实验，但只能通过与观察一致的推测思维得出。理想化的实验永远无法真正进行，尽管它可以导致对真实实验的深刻理解。

derived directly from experiment, but only by speculative thinking consistent with observation. The idealized experiment can never be actually performed, although it leads to a profound understanding o f real experiments.

在我们周围世界的各种复杂运动中，我们选择匀速运动作为第一个例子。这是最简单的，因为没有外力作用。然而，匀速运动永远无法实现；从塔上扔下的石头、沿路推的车永远不可能绝对匀速地移动，因为我们无法消除外力的影响。

From the variety o f complex motions in the world around us we choose as our first example uniform motion. This is the simplest, because there are no external forces acting. Uniform motion can, however, never be realized; a stone thrown from a tower, a cart pushed along a road can never move absolutely uniformly because we cannot eliminate the influence of external forces.

在一个精彩的悬疑故事中，最明显的线索往往会导致错误的嫌疑人。同样，当我们试图理解自然法则时，我们会发现最明显的直觉解释往往是错误的。

In a good mystery story the most obvious clues often lead to the wrong suspects. In our attempts to understand the laws of nature we find, similarly, that the most obvious intuitive explanation is often the wrong one.

人类的思维创造了不断变化的宇宙图景。伽利略的贡献在于摧毁了直觉的观点，并用新的观点取而代之。这就是伽利略发现的意义。

Hum an thought creates an ever-changing picture of the universe. Galileo’s contribution was to destroy the intuitive view and replace it by a new one. This is the significance of Galileo’s discovery.

但关于运动的另一个问题马上就出现了。如果速度不能表明作用于物体的外力，那什么能表明外力呢？伽利略找到了这个基本问题的答案，牛顿则给出了更简洁的答案，这为我们的研究提供了进一步的线索。

But a further question concerning motion arises immediately. I f the velocity is no indication of the external forces acting on a body, what is? The answer to this fundamental question was found by Galileo and still more concisely by Newton, and forms a further clue in our investigation.

为了找到正确的答案，我们必须更深入地思考在一条完全平坦的道路上行驶的车子。

T o find the correct answer we must think a little more deeply about the cart on a perfectly smooth road.

在我们理想化的实验中，运动的均匀性是由于没有任何外力造成的。现在让我们想象一下，给匀速运动的手推车一个沿运动方向的推力。现在会发生什么？显然，它的速度增加了。同样明显的是，沿与运动方向相反的方向推会降低速度。在第一种情况下，手推车因推力而加速，在第二种情况下，手推车减速或减慢。立即得出一个结论：外力的作用会改变速度。因此，推或拉的结果不是速度本身，而是速度的变化。这种力根据其作用方向是运动方向还是反方向，增加或减少速度。伽利略清楚地看到了这一点，并在他的《两门新科学》中写道：

In our idealized experiment the uniformity of the motion was due to the absence of all external forces. Let us now imagine that the uniformly moving cart is given a push in the direction o f the motion. What happens now? Obviously its speed is increased. Ju st as obviously, a push in the direction opposite to that o f the motion would decrease the speed. In the first case the cart is accelerated by the push, in the second case decelerated, or slowed down. A conclusion follows at once: the action o f an external force changes the velocity. Thus not the velocity itself but its change is a consequence o f pushing or pulling. Such a force either increases or decreases the velocity according to whether it acts in the direction o f motion or in the opposite direction. Galileo saw this clearly and wrote in his Two New Sciences:

...一旦赋予运动物体任何速度，只要消除加速或减速的外部原因，该速度就会严格保持，这种情况只出现在水平面上；因为在向下倾斜的平面上，已经存在加速的原因；而在向上倾斜的平面上，则存在减速的原因；由此可知，沿水平面的运动是永恒的；因为如果速度均匀，它就不会减小或减慢，更不用说消灭了。

. . . any velocity once imparted to a moving body will be rigidly maintained as long as the external causes of acceleration or retardation are removed, a condition which is found only on horizontal planes; for in the case of planes which slope downwards there is already present a cause of acceleration; while on planes sloping upwards there is retardation; from this it follows that motion along a horizontal plane is perpetual; for, if the velocity be uniform, it cannot be diminished or slackened, much less destroyed.

通过遵循正确的线索，我们可以更深入地理解运动问题。力和速度变化之间的联系——而不是我们直觉认为的力和速度本身之间的联系——是

By following the right clue we achieve a deeper understanding o f the problem o f motion. The connection between force and the change of velocity— and not, as we should think according to our intuition, the connection between force and the velocity itself—is

牛顿所制定的经典力学的基础。

the basis o f classical mechanics as formulated by Newton.

我们一直在使用经典力学中起主要作用的两个概念：力和速度变化。在科学的进一步发展中，这两个概念都得到了扩展和概括。因此，必须更仔细地研究它们。

We have been making use of two concepts which play principal roles in classical mechanics: force and change of velocity. In the further development of science both of these concepts are extended and generalized. They must, therefore, be examined more closely.

什么是力？我们直观地感受到这个词的含义。这个概念源于推、投、拉的努力——源于伴随这些动作的肌肉感觉。但它的概括远远超出了这些简单的例子。我们甚至不需要想象一匹拉车的马拉车，就可以想到力！我们谈论太阳和地球、地球和月亮之间的引力，以及引起潮汐的力。我们谈论地球迫使我们和我们周围的所有物体保持在它的影响范围内的力，以及风在海面上掀起波浪或吹动树叶的力。当我们观察到速度发生变化时，一般意义上的外力就是罪魁祸首。

W hat is force? Intuitively, we feel what is meant by this term. The concept arose from the effort o f pushing, throwing or pulling— from the muscular sensation accompanying each of these acts. But its generalization goes far beyond these simple examples. We can think of force even without picturing a horse pulling a carriage! We speak of the force o f attraction between the sun and the earth, the earth and the moon, and of those forces which cause the tides. We speak o f the force by which the earth compels ourselves and all the objects about us to remain within its sphere of influence, and of the force with which the wind makes waves on the sea, or moves the leaves of trees. When and where we observe a change in velocity, an external force, in the general sense, must be held responsible.

牛顿在他的 《自然哲学的数学原理》中写道：

Newton wrote in his Principia:

施加的力是作用于物体的一种作用，目的是改变其状态，无论是静止状态，还是沿直线均匀向前运动的状态。

An impressed force is an action exerted upon a body, in order to change its state, either of rest, or of moving uniformly forward in a right line.

这种力只存在于动作中；动作结束后，它不再存在于物体中。因为物体保持它所获得的每个新状态，仅靠它的惯性。外加力有不同的来源；例如来自撞击、压力、向心力。

This force consists in the action only; and remains no longer in the body, when the action is over. For a body maintains every new state it acquires, by its vis inertiae only. Impressed forces are of different origins; as from percussion, from pressure, from centripetal force.

如果一块石头从塔顶落下，它的运动绝不是均匀的；石头下落时速度会增加。我们得出结论：有一个外力作用于运动方向。或者换句话说：地球吸引着石头。让我们再举一个例子。当一块石头垂直向上抛出时会发生什么？速度会减小，直到石头到达最高点并开始下落。速度减小是由与下落物体的加速度相同的力引起的。在一种情况下，力作用于运动方向，在另一种情况下则作用于相反方向。力是相同的，但它会导致加速或减速，具体取决于石头是下落还是向上抛出。

I f a stone is dropped from the top o f a tower its motion is by no means uniform; the velocity increases as the stone falls. We conclude: an external force is acting in the direction o f the motion. O r, in other words: the earth attracts the stone. Let us take another example. What happens when a stone is thrown straight upward? The velocity decreases until the stone reaches its highest point and begins to fall. This decrease in velocity is caused by the same force as the acceleration o f a falling body. In one case the force acts in the direction of the motion, in the other case in the opposite direction. The force is the same, but it causes acceleration or deceleration according to whether the stone is dropped or thrown upward.

向量

V E C T O R S

我们一直在考虑的所有运动都是直线运动，即沿直线运动。现在我们必须更进一步。通过分析最简单的情况，并在最初的尝试中排除所有复杂的复杂因素，我们就能理解自然法则。直线比曲线简单。然而，仅仅理解直线运动是不可能满足的。月球、地球和行星的运动，正是力学原理在它们身上得到了如此辉煌的成功，它们都是沿曲线路径的运动。从直线运动转变为沿曲线路径的运动带来了新的困难。如果我们想理解这些原理，就必须有勇气克服它们。

A ll motions we have been considering are rectilinear, that is, along a straight line. Now we must go one step farther. We gain an understanding of the laws of nature by analysing the simplest cases and by leaving out o f our first attempts all intricate complications. A straight line is simpler than a curve. It is, however, impossible to be satisfied with an understanding of rectilinear motion alone. The motions of the moon, the earth and the planets, just those to which the principles of mechanics have been applied with such brilliant success, are motions along curved paths. Passing from rectilinear motion to motion along a curved path brings new difficulties. We must have the courage to overcome them if we wish to understand the principles

十三

经典力学给了我们最初的线索，从而成为科学发展的起点。

of classical mechanics which gave us the first clues and so formed the starting-point for the development of science.

让我们考虑另一个理想化的实验，其中一个完美的球体在光滑的桌面上均匀滚动。我们知道，如果给球体一个推力，即施加一个外力，速度就会改变。现在假设冲击的方向不是像手推车的例子那样沿着运动线，而是沿着一个完全不同的方向，比如说垂直于运动线。球体会发生什么情况？

Let us consider another idealized experiment, in which a perfect sphere rolls uniformly on a smooth table. We know that if the sphere is given a push, that is, i f an external force is applied, the velocity will be changed. Now suppose that the direction of the blow is not, as in the example of the cart, in the line of motion, but in a quite different direction, say, perpendicular to that line. What happens to the sphere?

运动可分为三个阶段：起始运动、力的作用和力停止作用后的最终运动。根据惯性定律，力作用前后的速度都是完全均匀的。但是，力作用前后的均匀运动有一个区别：方向会改变。球体的起始路径与力的方向互相垂直。最终运动不会沿着这两条线中的任何一条，而是在它们之间的某个地方，如果打击力度大而初速度小，则运动更接近力的方向；如果打击力度小而初速度大，则运动更接近原来的运动路线。我们根据惯性定律得出的新结论是：一般来说，外力的作用不仅会改变速度，还会改变运动的方向。理解这一事实使我们为矢量概念引入物理学的概括做好了准备。

Three stages of the motion can be distinguished: the initial motion, the action o f the force, and the final motion after the force has ceased to act. According to the law of inertia, the velocities before and after the action of the force are both perfectly uniform. But there is a difference between the uniform motion before and after the action of the force: the direction is changed. The initial path of the sphere and the direction of the force are perpendicular to each other. The final motion will be along neither of these two lines, but somewhere between them, nearer the direction of the force if the blow is a hard one and the initial velocity small, nearer the original line of motion if the blow is gentle and the initial velocity great. O ur new conclusion, based on the law of inertia, is: in general the action of an external force changes not only the speed but also the direction of the motion. A n understanding o f this fact prepares us for the generalization introduced into physics by the concept o f vectors.

我们可以继续使用我们直截了当的推理方法。起点仍然是伽利略的惯性定律。我们还远没有穷尽这一宝贵线索对运动之谜的推论。

We can continue to use our straightforward method o f reasoning. The starting-point is again Galileo’s law o f inertia. We are still far from exhausting the consequences o f this valuable clue to the puzzle o f motion.

让我们考虑两个球体在光滑桌面上朝不同方向运动的情况。为了有一个明确的图像，我们可以假设两个方向互相垂直。由于没有外力作用，运动是完全均匀的。进一步假设速度相等，即在相同的时间间隔内，两者覆盖相同的距离。但是，说两个球体有相同的速度是正确的吗？答案可以是肯定的，也可以是否定的！如果两辆汽车的速度表都显示每小时四十英里，我们通常会说它们有相同的速度，不管它们朝哪个方向行驶。但是科学必须为自己使用而创造自己的语言、自己的概念。科学概念通常始于普通语言中用于日常生活事务的概念，但它们的发展却截然不同。

Let us consider two spheres moving in different directions on a smooth table. So as to have a definite picture, we may assume the two directions perpendicular to each other. Since there are no external forces acting, the motions are perfectly uniform. Suppose, further, that the speeds are equal, that is, both cover the same distance in the same interval o f time. But is it correct to say that the two spheres have the same velocity? The answer can be yes or n o ! I f the speedometers of two cars both show forty miles per hour, it is usual to say that they have the same speed or velocity, no matter in which direction they are travelling. But science must create its own language, its own concepts, for its own use. Scientific concepts often begin with those used in ordinary language for the affairs, o f everyday life, but they develop quite differently.

它们经过转化，失去了普通语言中的歧义性，变得更加严谨，从而可以应用于科学思想。

They are transformed and lose the ambiguity associated with them in ordinary language, gaining in rigorousness so that they may be applied to scientific thought.

从物理学家的角度来看，说两个球体在不同方向上运动的速度不同是有利的。虽然这纯粹是惯例问题，但更方便的说法是，四辆汽车从不同道路上的同一交通环岛行驶时的速度并不相同

From the physicist’s point o f view it is advantageous to say that the velocities of the two spheres moving in different directions are different. Although purely a matter of convention, it is more convenient to say that four cars travelling away from the same traffic roundabout on different roads do not have the same velocity

尽管速度表上显示的速度都是 40 英里每小时。速度和速率之间的这种区别说明了物理学如何从日常生活中使用的概念开始，对其进行改变，并最终使科学得到长足发展。

even though the speeds, as registered on the speedometers, are all forty miles per hour. This differentiation between speed and velocity illustrates how physics, starting with a concept used in everyday life, changes it in a way which proves fruitful in the further development o f science.

如果测量长度，结果将以单位数表示。一根棍子的长度可能是 3 英尺 7 英寸；某个物体的重量可能是 2 磅 3 盎司；测量的时间间隔可能是很多分钟或几秒。在每种情况下，测量结果都用数字表示。然而，单靠数字不足以描述某些物理概念。对这一事实的认识标志着科学研究的显著进步。例如，方向和数字对于表征速度至关重要。这种既具有大小又具有方向的量称为矢量。矢量的适当符号是

I f a length is measured, the result is expressed as a number of units. The length of a stick may be 3 ft. 7 in .; the weight of some object 2 lb. 3 oz.; a measured time interval so many minutes or seconds. In each of these cases the result of the measurement is expressed by a number. A number alone is, however, insufficient for describing some physical concepts. The recognition of this fact marked a distinct advance in scientific investigation. A direction as well as a number is essential for the characterization o f a velocity, for example. Such a quantity, possessing both magnitude and direction, is called a vector. A suitable symbol for

1 6

它是一根箭头。速度可以用箭头来表示，或者简单地说，用一个矢量来表示，矢量的长度以某个选定的单位尺度来衡量速度，矢量的方向就是运动的方向。

it is an arrow. Velocity may be represented by an arrow or, briefly speaking, by a vector whose length in some chosen scale of units is a measure of the speed, and whose direction is that of the motion.

如果有四辆汽车以相同的速度从环形交叉路口分出，它们的速度可以用四个相同长度的矢量表示，如我们上一张图所示。

I f four cars diverge with equal speed from a traffic roundabout, their velocities can be represented by four vectors o f the same length, as seen from our last drawing.

在所使用的比例中，一英寸代表 40 米/小时，这样，任何速度都可以用矢量表示，相反，如果已知比例，则可以从这样的矢量图中确定速度。

In the scale used, one inch stands for 40 m .p.h. In this way any velocity may be denoted by a vector, and conversely, if the scale is known, one may ascertain the velocity from such a vector diagram.

如果两辆车在高速公路上相遇，并且它们的速度表都显示 40 英里/小时，我们用两个不同的矢量来表示它们的速度，箭头指向相反的方向。同样，指示

I f two cars pass each other on the highway and their speedometers both show 40 m .p .h., we characterize their velocities by two different vectors with arrows pointing in opposite directions. So also the arrows indicating

纽约的“上城区”和“下城区”地铁列车必须指向相反的方向。但所有以相同速度在不同车站或不同大道上行驶的上城区列车都具有相同的速度，这可以用一个矢量表示。矢量无法指示列车经过哪些车站或在多条平行轨道中的哪条轨道上运行。换句话说，根据公认的惯例，所有此类矢量（如下图所示）可视为相等；它们位于同一条或平行的线上，长度相等，最后带有箭头

“ uptown” and “ downtown” subway trains in New York must point in opposite directions. But all trains moving uptown at different stations or on different avenues with the same speed have the same velocity, which may be represented by a single vector. There is nothing about a vector to indicate which stations the train passes or on which o f the many parallel tracks it is running. In other words, according to the accepted convention, all such vectors, as drawn below, may be regarded as equal; they lie along the same or parallel lines, are o f equal length, and finally, have arrows

1 7

指向同一方向。下图中显示的向量全都不同，因为它们的长度或方向不同，或两者兼而有之。同样的四个向量可以用另一种方式绘制，它们全都偏离

pointing in the same direction. The next figure shows vectors all different, because they differ either in length or direction, or both. The same four vectors may be drawn in another way, in which they all diverge from

一个共同点。由于起点并不重要，这些向量可以表示四辆汽车从同一交通环岛离开的速度，或者表示四辆汽车在该国不同地区以指示速度沿指示方向行驶的速度。

a common point. Since the starting-point does not matter, these vectors can represent the velocities o f four cars moving away from the same traffic roundabout, or the velocities of four cars in different parts o f the country travelling with the indicated speeds in the indicated directions.

现在可以使用这种矢量表示来描述先前讨论过的有关直线运动的事实。我们谈到一辆手推车，它沿直线匀速移动，并在其运动方向上受到推力，从而增加其速度。从图形上讲，这可以用两个矢量表示，较短的矢量表示推力之前的速度，而较长的矢量在同一方向上表示推力之后的速度。虚线矢量的含义很清楚；它表示速度的变化，正如我们所知，推力是造成速度变化的原因。对于力的方向与运动相反的情况，即运动减慢的情况，图表会有所不同。

This vector representation may now be used to describe the facts previously discussed concerning rectilinear motion. We talked of a cart, moving uniformly in a straight line and receiving a push in the direction o f its motion which increases its velocity. Graphically this may be represented by two vectors, a shorter one denoting the velocity before the push and a longer one in the same direction denoting the velocity after the push. The meaning o f the dotted vector is clear; it represents the change in velocity for which, as we know, the push is responsible. For the case where the force is directed against the motion, where the motion is slowed down, the diagram is somewhat different.

同样，虚线矢量对应于速度的变化，但在这种情况下，它的方向不同。很明显，不仅速度本身，而且它们的变化都是矢量。但速度的每一个变化都是

Again the dotted vector corresponds to a change in velocity, but in this case its direction is different. It is clear that not only velocities themselves but also their changes are vectors. But every change in velocity is

由于外力的作用，力也必须用矢量表示。为了描述力，仅仅说明我们推车的力度是不够的；我们还必须说明我们推车的方向。力，如速度或其变化，必须用矢量表示，而不能只用数字表示。因此：外力也是矢量，并且必须与速度变化的方向相同。

due to the action o f an external force; thus the force must also be represented by a vector. In order to characterize a force it is not sufficient to state how hard we push the cart; we must also say in which direction we push. The force, like the velocity or its change, must be represented by a vector and not by a number alone. Therefore: the external force is also a vector, and must have the same direction as the change in velocity.

在这两幅图中，虚线矢量真实地显示了力的方向，也显示了速度的变化。

In the two drawings the dotted vectors show the direction o f the force as truly as they indicate the change in velocity.

怀疑论者可能会说，他认为引入向量没有任何好处。所完成的一切只是将先前公认的事实翻译成一种陌生而复杂的语言。在这个阶段，确实很难说服他自己错了。目前，他实际上是对的。但我们将会看到，正是这种奇怪的语言导致了一个重要的概括，其中向量似乎是必不可少的。

Here the sceptic may remark that he sees no advantage in the introduction o f vectors. A ll that has been accomplished is the translation of previously recognized facts into an unfamiliar and complicated language. A t this stage it would indeed be difficult to convince him that he is wrong. For the moment he is, in fact, right. But we shall see that just this strange language leads to an important generalization in which vectors appear to be essential.

热动力

T H E R ID D L E O F M O T IO N

只要我们只处理沿直线的运动，我们就远远不能理解自然界中观察到的运动。我们必须考虑沿曲线路径的运动，下一步就是确定支配这种运动的规律。这不是一件容易的事。在直线运动的情况下，我们的速度、速度变化和力的概念被证明是最有用的。但我们并没有立即看到如何将它们应用于

So long as we deal only with motion along a straight line, we are far from understanding the motions observed in nature. We must consider motions along curved paths, and our next step is to determine the laws governing such motions. This is no easy task. In the case o f rectilinear motion our concepts of velocity, change o f velocity, and force proved most useful. But we do not immediately see how we can apply them to

2 0

沿着曲线路径运动。确实可以想象，旧概念不适合描述一般运动，必须创建新概念。我们是应该尝试遵循旧路径，还是寻找新路径？

motion along a curved path. It is indeed possible to imagine that the old concepts are unsuited to the description o f general motion, and that new ones must be created. Should we try to follow our old path, or seek a new one?

概念的泛化是科学中经常使用的一种过程。泛化的方法并不唯一，因为通常有多种方法可以实现。但必须严格满足一个要求：任何广义的概念在满足原始条件时都必须归结为原始概念。

T he generalization of a concept is a process very often used in science. A method of generalization is not uniquely determined, for there are usually numerous ways o f carrying it out. O ne requirement, however, must be rigorously satisfied: any generalized concept must reduce to the original one when the original conditions are fulfilled.

我们可以通过现在正在处理的例子来最好地解释这一点。我们可以尝试将速度、速度变化和力的旧概念概括为沿曲线路径运动的情况。从技术上讲，当谈到曲线时，我们包括直线。

We can best explain this by the example with which we are now dealing. We can try to generalize the old concepts of velocity, change o f velocity, and force for the case of motion along a curved path. Technically, when speaking o f curves, we include straight lines.

直线是曲线的一个特殊而又平凡的例子。因此，如果为沿曲线的运动引入速度、速度变化和力，那么它们也会自动为沿直线的运动引入。但这一结果不应与先前得到的结果相矛盾。如果曲线变成直线，所有广义的概念都必须归结为描述直线运动的熟悉概念。但这一限制不足以唯一地确定概括。它留下了许多可能性。科学史表明，最简单的概括有时成功，有时失败。我们必须首先做出猜测。在我们的例子中，它是

The straight line is a special and trivial example o f a curve. If, therefore, velocity, change in velocity, and force are introduced for motion along a curved line, then they are automatically introduced for motion along a straight line. But this result must not contradict those results previously obtained. I f the curve becomes a straight line, all the generalized concepts must reduce to the familiar ones describing rectilinear motion. But this restriction is not sufficient to determine the generalization uniquely. It leaves open many possibilities. The history o f science shows that the simplest generalizations sometimes prove successful and sometimes not. We must first make a guess. In our case it is

猜测正确的概括方法是一件简单的事情。新概念被证明非常成功，并帮助我们理解抛出的石头的运动以及行星的运动。

a simple matter to guess the right method o f generalization. The new concepts prove very successful and help us to understand the motion o f a thrown stone as well as that of the planets.

那么，在一般的曲线运动情况下，速度、速度变化和力这些词到底是什么意思呢？让我们从速度开始。一个非常小的物体沿着曲线从左向右运动。这么小的物体通常被称为粒子。图中曲线上的点表示粒子在某一时刻的位置。与这个时间和位置相对应的速度是多少？伽利略的线索再次暗示了一种引入速度的方法。我们必须再次发挥想象力，思考一个理想化的实验。粒子在外力的作用下沿着曲线从左向右移动。想象一下，在某一时刻，在点所指示的点，所有这些力突然停止作用。那么，根据惯性定律，运动必定是均匀的。当然，在实践中，我们永远无法完全让物体摆脱所有外部影响。我们只能推测“如果……会发生什么？” ”，并根据从中得出的结论以及它们与实验的一致性来判断我们猜测的恰当性。

And now just what do the words velocity, change in velocity, and force mean in the general case of motion along a curved line? Let us begin with velocity. Along the curve a very small body is moving from left to right. Such a small body is often called a particle. The dot on the curve in our drawing shows the position of the particle at some instant o f time. What is the velocity corresponding to this time and position? Again Galileo’s clue hints at a way o f introducing the velocity. We must, once more, use our imagination and think about an idealized experiment. The particle moves along the curve, from left to right, under the influence o f external forces. Imagine that at a given time, and at the point indicated by the dot, all these forces suddenly cease to act. Then, the motion must, according to the law o f inertia, be uniform. In practice we can, of course, never completely free a body from all external influences. We can only surmise “ what would happen i f . . . ? ” and judge the pertinence of our guess by the conclusions which can be drawn from it and by their agreement with experiment.

下图中的矢量表示如果所有外力都消失，匀速运动的猜测方向。它是所谓的切线方向。通过显微镜观察运动的粒子，我们会看到曲线的很小一部分，它看起来就像一小段。切线是它的延长。因此，所画的矢量表示给定时刻的速度。速度矢量位于切线上。它的长度表示速度的大小，或者例如汽车速度表指示的速度。

The vector in the next drawing indicates the guessed direction of the uniform motion if all external forces were to vanish. It is the direction of the so-called tangent. Looking at a moving particle through a microscope one sees a very small part of the curve, which appears as a small segment. The tangent is its prolongation. Thus the vector drawn represents the velocity at a given instant. The velocity vector lies on the tangent. Its length represents the magnitude of the velocity, or the speed as indicated, for instance, by the speedometer of a car.

我们为了找到速度矢量而破坏运动的理想化实验不应该太当真。它只能帮助我们理解我们所谓的速度矢量，并使我们能够在给定时刻的给定点确定它。

O ur idealized experiment about destroying the motion in order to find the velocity vector must not be taken too seriously. It only helps us to understand what we should call the velocity vector and enables us to determine it for a given instant at a given point.

下图显示了沿曲线移动的粒子的三个不同位置的速度矢量。在这种情况下，不仅方向，而且速度的大小（由矢量的长度表示）在运动过程中也会发生变化。

In the next drawing, the velocity vectors for three different positions of a particle moving along a curve are shown. In this case not only the direction but the magnitude of the velocity, as indicated by the length of the vector, varies during the motion.

这种新的速度概念是否满足所有概括的要求？即：如果曲线变成直线，它是否就归结为熟悉的概念？显然是的。直线的切线就是直线本身。速度矢量位于运动线上，就像移动的推车或滚动的球体一样。

Does this new concept o f velocity satisfy the requirement formulated for all generalizations? T hat is: does it reduce to the familiar concept if the curve becomes a straight line? Obviously it does. The tangent to a straight line is the line itself. The velocity vector lies in the line of the motion, just as in the case o f the moving cart or the rolling spheres.

下一步是引入沿曲线移动的粒子的速度变化。这也可以以各种方式实现，我们从中选择最简单、最方便的方式。最后一张图显示了几个速度矢量，表示路径上各个点的运动。前两个可以再次绘制，这样它们就有一个共同的起点，正如我们已经看到的那样，使用矢量是可能的。

The next step is the introduction o f the change in velocity of a particle moving along a curve. This also may be done in various ways, from which we choose the simplest and most convenient. The last drawing showed several velocity vectors representing the motion at various points along the path. The first two of these may be drawn again so that they have a common starting-point, as we have seen is possible with vectors.

我们称虚线矢量为速度变化。它的起点是第一个矢量的终点，它的端点是第二个矢量的终点。速度变化的这个定义乍一看似乎是人为的，毫无意义。在矢量 (1) 和 (2) 方向相同的特殊情况下，它会变得更加清晰。当然，这意味着要转到直线运动的情况。如果两个矢量具有相同的起点，虚线矢量再次连接它们的端点。现在的图画与第 18 页上的图画相同，

The dotted vector we call the change in velocity. Its starting-point is the end of the first vector and its endpoint the end of the second vector. This definition of the change in velocity may, at first sight, seem artificial and meaningless. It becomes much clearer in the special case in which vectors (1) and (2) have the same direction. This, o f course, means going over to the case of straight-line motion. I f both vectors have the same initial point, the dotted vector again connects their endpoints. The drawing is now identical with that on p. 18,

并且先前的概念作为新概念的一个特例被重新获得。我们可以注意到，我们必须在绘图中将这两条线分开，否则它们就会重合并且难以区分。

and the previous concept is regained as a special case o f the new one. We may remark that we had to separate the two lines in our drawing, since otherwise they would coincide and be indistinguishable.

现在我们必须迈出概括过程的最后一步。这是我们迄今为止所做的所有猜测中最重要的一步。必须建立力和速度变化之间的联系，以便我们能够提出线索，使我们能够理解运动的一般问题。

We now have to take the last step in our process of generalization. It is the most important o f all the guesses we have had to make so far. T he connection between force and change in velocity has to be established so that we can formulate the clue which will enable us to understand the general problem o f motion.

解释直线运动的线索很简单：外力导致速度变化；力矢量的方向与变化方向相同。那么现在什么可以被视为曲线运动的线索呢？完全一样！唯一的区别是速度变化现在比以前具有更广泛的含义。看一眼最后两幅图的虚线矢量，就可以清楚地看到这一点。

T he clue to an explanation o f motion along a straight line was simple: external force is responsible for change in velocity; the force vector has the same direction as the change. A nd now what is to be regarded as the clue to curvilinear motion? Exactly the sam e! The only difference is that change of velocity has now a broader meaning than before. A glance at the dotted vectors of the last two drawings shows this point clearly.

如果已知曲线上所有点的速度，那么可以立即推断出任何一点的力的方向。必须绘制两个瞬间的速度矢量，这两个瞬间相隔很短的时间间隔，因此它们的位置非常接近。从第一个端点到第二个端点的矢量表示作用力的方向。但重要的是，这两个速度矢量

I f the velocity is known for all points along the curve, the direction o f the force at any point can be deduced at once. O ne must draw the velocity vectors for two instants separated by a very short time interval and therefore corresponding to positions very near each other. T he vector from the end-point o f the first to that o f the second indicates the direction o f the acting force. But it is essential that the two velocity vectors

二十五

应该只隔着一个“非常短”的时间间隔。对“非常近”、“非常短”等词的严格分析远非易事。事实上，正是这种分析让牛顿和莱布尼茨发现了微分学。

should be separated only by a “ very short” time interval. The rigorous analysis o f such words as “ very near” , “ very short” is far from simple. Indeed it was this analysis which led Newton and Leibnitz to the discovery of differential calculus.

这是一条漫长而复杂的道路，它通向伽利略线索的概括。我们无法在此展示这一概括的后果有多么丰富和富有成效。它的应用导致了许多以前不连贯和误解的事实得到简单而令人信服的解释。

It is a tedious and elaborate path which leads to the generalization o f Galileo’s clue. We cannot show here how abundant and fruitful the consequences o f this generalization have proved. Its application leads to simple and convincing explanations o f many facts previously incoherent and misunderstood.

我们从极其丰富的动议种类中只选取最简单的一种，并运用刚刚制定的定律来解释它们。

From the extremely rich variety o f motions we shall take only the simplest and apply to their explanation the law just formulated.

枪中射出的子弹、以一定角度投掷的石头、从软管中喷出的水流，都描绘出同一种类型的熟悉路径——抛物线。例如，想象一下将测速仪连接到石头上，这样就可以绘制出任意时刻的速度矢量。

A bullet shot from a gun, a stone thrown at an angle, a stream of water emerging from a hose, all describe familiar paths o f the same type— the parabola. Imagine a speedometer attached to a stone, for example, so that its velocity vector may be drawn for any instant.

结果很可能就是上图所示的结果。作用在石头上的力的方向就是速度变化的方向，我们已经看到了如何确定它。下图所示的结果表明，力是垂直的，

The result may well be that represented in the above drawing. The direction o f the force acting on the stone is just that of the change in velocity, and we have seen how it may be determined. The result, shown in the next drawing, indicates that the force is vertical, and

二十六

向下。这与让一块石头从塔顶落下完全一样。路径完全不同，速度也不同，但速度变化的方向相同，即朝向地球中心。

directed downward. It is exactly the same as when a stone is allowed to fall from the top o f a tower. The paths are quite different, as also are the velocities, but the change in velocity has the same direction, that is, toward the centre o f the earth.

一块石头绑在一根绳子的一端，在水平面上摆动，沿圆形路径移动。

A stone attached to the end of a string and swung around in a horizontal plane moves in a circular path.

如果速度均匀，则表示该运动的图中的所有矢量都具有相同的长度。

A ll the vectors in the diagram representing this motion have the same length if the speed is uniform.

然而，速度并不均匀，因为路径不是直线。只有在均匀的直线运动中，

Nevertheless, the velocity is not uniform, for the path is not a straight line. O nly in uniform, rectilinear mo-

二十七

那里没有力。但在这里，有力，速度不是在大小上改变，而是在方向上改变。根据运动定律，一定有某种力导致这种变化，在本例中是石头和握着绳子的手之间的力。另一个问题立刻出现了：力作用于哪个方向？矢量图再次显示了答案。画出两个非常接近的点的速度矢量，并发现速度变化。可以看出，最后一个矢量沿着绳子指向圆心，并且始终垂直于速度矢量或切线。换句话说，手通过绳子对石头施加了力。

tion are there no forces involved. Here, however, there are, and the velocity changes not in magnitude but in direction. According to the law of motion there must be some force responsible for this change, a force in this case between the stone and the hand holding the string. A further question arises immediately: in what direction does the force act? Again a vector diagram shows the answer. The velocity vectors for two very near points are drawn, and the change of velocity found. This last vector is seen to be directed along the string toward the centre of the circle, and is always perpendicular to the velocity vector, or tangent. In other words, the hand exerts a force on the stone by means o f the string.

月球绕地球公转这个更重要的例子非常类似。这可以近似地表示为匀速圆周运动。力朝向地球的原因与我们前面例子中朝向手的原因相同。地球和月球之间没有线连接，但我们可以想象两个物体中心之间有一条线；力沿着这条线指向地球中心，就像抛在空中或从塔上掉下来的石头受到的力一样。

Very similar is the more important example of the revolution of the moon around the earth. This may be represented approximately as uniform circular motion. The force is directed toward the earth for the same reason that it was directed toward the hand in our former example. There is no string connecting the earth and the moon, but we can imagine a line between the centres o f the two bodies; the force lies along this line and is directed toward the centre of the earth, just as the force on a stone thrown in the air or dropped from a tower.

二十八

我们关于运动的所有内容都可以用一句话来概括。 力和速度变化 是具有相同方向的矢量。这是运动问题的最初线索，但它肯定不足以彻底解释观察到的所有运动。从亚里士多德的思路到伽利略的思路的转变形成了科学基础中最重要的基石。一旦做出这一突破，进一步发展的路线就很清晰了。我们在这里的兴趣在于发展的最初阶段，在于追随最初的线索，在于展示新的物理概念是如何在与旧观念的痛苦斗争中诞生的。我们只关心科学的先驱工作，包括寻找新的和意想不到的发展道路；关心科学思想的冒险，它们创造了一幅不断变化的宇宙图景。最初和基本的步骤总是具有革命性。科学想象力发现旧概念太局限，并用新概念取而代之。沿着任何已经开始的路线继续发展，更具有进化的性质，直到达到下一个转折点，那时必须征服一个更新的领域。然而，为了理解是什么原因和什么困难迫使重要概念发生变化，我们不仅必须知道最初的线索，还必须知道可以得出的结论。

A ll that we have said concerning motion can be summed up in a single sentence. Force and change o f velocity are vectors having the same direction. This is the initial clue to the problem o f motion, but it certainly does not suffice for a thorough explanation of all motions observed. The transition from Aristotle’s line o f thought to that o f Galileo formed a most important corner-stone in the foundation o f science. Once this break was made, the line o f further development was clear. O u r interest here lies in the first stages of development, in following initial clues, in showing how new physical concepts are born in the painful struggle with old ideas. We are concerned only with pioneer work in science, which consists o f finding new and unexpected paths of development; with the adventures in scientific thought which create an ever-changing picture of the universe. The initial and fundamental steps are always o f a revolutionary character. Scientific imagination finds old concepts too confining, and replaces them by new ones. The continued development along any line already initiated is more in the nature of evolution, until the next turning point is reached when a still newer field must be conquered. In order to understand, however, what reasons and what difficulties force a change in important concepts, we must know not only the initial clues, but also the conclusions which can be drawn.

现代物理学最重要的特征之一是从最初的线索得出的结论不仅是定性的，而且是定量的。让我们

O ne of the most important characteristics o f modem physics is that the conclusions drawn from initial clues are not only qualitative but also quantitative. Let us

二十九

再考虑一下从塔上掉下来的一块石头。我们已经看到，它下落的速度会增加，但我们想知道更多。这种变化到底有多大？

again consider a stone dropped from a tower. We have seen that its velocity increases as it falls, but we should like to know much more. Ju st how great is this change?

石头开始下落后，它的位置和速度是多少？我们希望能够预测事件，并通过实验确定观察结果是否证实了这些预测，从而证实了最初的假设。

And what is the position and the velocity o f the stone at any time after it begins to fall? We wish to be able to predict events and to determine by experiment whether observation confirms these predictions and thus the initial assumptions.

为了得出定量结论，我们必须使用数学语言。大多数科学的基本思想本质上都很简单，而且通常可以用人人都能理解的语言来表达。要追查这些思想，需要掌握高度精细的调查技术。

To draw quantitative conclusions we must use the language of mathematics. Most o f the fundamental ideas o f science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone. T o follow up these ideas demands the knowledge of a highly refined technique o f investigation.

如果我们希望得出可以与实验相比较的结论，数学作为推理工具是必要的。只要我们只关注基本的物理思想，我们就可以避免使用数学语言。由于我们在这些页面中始终如一地这样做，因此我们必须偶尔限制自己引用一些结果，而无需证明，这些结果对于理解进一步发展中出现的重要线索是必不可少的。放弃数学语言的代价是精确度的损失，以及有时必须引用结果而不说明它们是如何得出的。

Mathematics as a tool o f reasoning is necessary if we wish to draw conclusions which may be compared with experiment. So long as we are concerned only with fundamental physical ideas we may avoid the language o f mathematics. Since in these pages we do this consistently, we must occasionally restrict ourselves to quoting, without proof, some o f the results necessary for an understanding o f important clues arising in the further development. The price which must be paid for abandoning the language o f mathematics is a loss in precision, and the necessity o f sometimes quoting results without showing how they were reached.

一个非常重要的运动例子是地球绕太阳的运动。众所周知，运动路径是一条封闭的曲线，称为椭圆。

A very important example o f motion is that of the earth around the sun. It is known that the path is a closed curve, called the ellipse. The construction o f a

三十

速度变化的矢量图显示，地球上的力指向太阳。但这毕竟是少量信息。我们希望能够预测任意时刻地球和其他行星的位置，我们希望预测下一次日食和许多其他天文事件的日期和持续时间。

vector diagram o f the change in velocity shows that the force on the earth is directed toward the sun. But this, after all, is scant inform ation. We should like to be able to predict the position o f the earth and the other planets for any arbitrary instant o f tim e, we should like to predict the date and duration o f the next solar eclipse and many other astronomical events.

这些事情是可以做到的，但不能仅仅基于我们最初的线索，因为现在不仅需要知道力的方向，还需要知道它的绝对值——它的大小。牛顿对这一点做出了有灵感的猜测。根据他的 引力定律，两个物体之间的吸引力简单地取决于它们之间的距离。距离越大，吸引力就越小。

It is possible to do these things, but not on the basis o f our initial clue alone, for it is now necessary to know not only the direction o f the force but also its absolute value—its m agnitude. It was Newton who made the inspired guess on this point. According to his law o f gravitation the force o f attraction between two bodies depends in a simple way on their distance from each other. It becomes smaller when the distance increases.

具体来说，如果距离增加一倍，它就会变小 2 x 2 = 4 倍，如果距离增加三倍，它就会变小 3 x 3 = 9 倍。

T o be specific it becomes 2 x 2 = 4 times smaller if the distance is doubled, 3 x 3 = 9 times smaller if the distance is made three times as great.

因此我们看到，在引力的情况下，我们成功地用一种简单的方式表达了

Thus we see that in the case o f gravitational force we have succeeded in expressing, in a simple way, the

力与运动物体之间距离的关系。在其他所有不同种类的力（例如电力、磁力等）起作用的情况下，我们也采取类似的方法。我们尝试使用力的简单表达式。只有当从中得出的结论得到实验证实时，这种表达式才是合理的。

dependence o f the force on the distance between the moving bodies. We proceed similarly in all other cases where forces o f different kinds— for instance, electric, magnetic, and the like— are acting. We try to use a simple expression for the force. Such an expression is justified only when the conclusions drawn from it are confirmed by experiment.

但仅凭对引力的了解还不足以描述行星的运动。我们已经看到，表示力的矢量和任何短时间间隔内速度的变化具有相同的方向，但我们必须更进一步追随牛顿，假设它们的长度之间存在简单的关系。假设所有其他条件相同，即相同的运动物体和在相等的时间间隔内考虑的变化，那么根据牛顿的说法，速度的变化与力成正比。

But this knowledge o f the gravitational force alone is not sufficient for a description o f the motion o f the planets. We have seen that vectors representing force and change in velocity for any short interval o f time have the same direction, but we must follow Newton one step farther and assume a simple relation between their lengths. Given all other conditions the same, that is, the same moving body and changes considered over equal time intervals, then, according to Newton, the change o f velocity is proportional to the force.

因此，只需要两个互补的猜测就可以得出有关行星运动的定量结论。一个是一般性的，说明力和速度变化之间的联系。另一个是特殊的，说明所涉及的特定力与物体之间距离的确切依赖关系。第一个是牛顿的一般运动定律，第二个是他的万有引力定律。它们共同决定了运动。这可以通过以下听起来有些笨拙的推理来阐明。

Thus just two complementary guesses are needed for quantitative conclusions concerning the motion o f the planets. O ne is of a general character, stating the connection between force and change in velocity. The other is special, and states the exact dependence o f the particular kind o f force involved on the distance between the bodies. The first is Newton’s general law of motion, the second his law of gravitation. Together they determine the motion. This can be made clear by the following somewhat clumsy-sounding reasoning.

假设在给定的时间内，行星的位置和速度可以确定，并且力是已知的。那么，根据牛顿定律，我们知道

Suppose that at a given time the position and velocity o f a planet can be determined, and that the force is known. Then, according to Newton’s laws, we know

速度变化 3

the change in velocity du 3

响一个短暂的时间间隔。

ring a short time interval.

知道了初速度及其变化，我们就能找到时间间隔结束时行星的速度和位置。通过不断重复这个过程，可以追踪整个运动路径，而无需进一步求助于观测数据。原则上，这是力学预测物体运动路线的方法，但这里使用的方法几乎不切实际。在实践中，这种逐步的过程会非常繁琐，而且不准确。幸运的是，这是完全没有必要的；数学提供了一条捷径，可以用比我们写一句话少得多的墨水精确描述运动。以这种方式得出的结论可以通过观察来证明或反驳。

Knowing the initial velocity and its change, we can find the velocity and position of the planet at the end o f the time interval. By a continued repetition of this process the whole path o f the motion may be traced without further recourse to observational data. This is, in principle, the way mechanics predicts the course of a body in motion, but the method used here is hardly practical. In practice such a step-by-step procedure would be extremely tedious as well as inaccurate. Fortunately, it is quite unnecessary; mathematics furnishes a short cut, and makes possible precise description of the motion in much less ink than we use for a single sentence. The conclusions reached in this way can be proved or disproved by observation.

在空中下落的石块的运动和月球在其轨道上的旋转中，都存在着同一种外力，即地球对物体的吸引力。牛顿认识到，下落的石块、月球和行星的运动只是作用于任何两个物体之间的万有引力的非常特殊的表现。在简单的情况下，运动可以用数学的帮助来描述和预测。在涉及许多物体相互作用的极端复杂的情况下，数学描述并不那么简单，但基本原理是相同的。

The same kind o f external force is recognized in the motion o f a stone falling through the air and in the revolution o f the moon in its orbit, namely, that o f the earth’s attraction for material bodies. Newton recognized that the motions o f falling stones, o f the moon, and of planets are only very special manifestations of a universal gravitational force acting between any two bodies. In simple cases the motion may be described and predicted by the aid of mathematics. In remote and extremely complicated cases, involving the action o f many bodies on each other, a mathematical description is not so simple, but the fundamental principles are the same.

我们发现，我们根据最初的线索得出的结论，在一个

We find the conclusions, at which we arrived by following our initial clues, realized in the motion o f a

在月球、地球和行星的运动中，被抛出的石头。

thrown stone, in the motion o f the moon, the earth, and the planets.

事实上，我们的整个猜测体系要么需要通过实验来证实，要么需要通过实验来推翻。任何假设都不能被孤立出来进行单独测试。

It is really our whole system o f guesses which is to be either proved or disproved by experiment. No one of the assumptions can be isolated for separate testing.

在行星围绕太阳运转的情况下，我们发现力学系统运转得十分出色。

In the case of the planets moving around the sun it is found that the system of mechanics works splendidly.

尽管如此，我们完全可以想象，基于不同假设的另一个系统也可能同样有效。

Nevertheless we can well imagine that another system, based on different assumptions, might work just as well.

物理概念是人类思维的自由创造，无论它看起来如何，它都不是外部世界唯一决定的。在我们努力理解现实的过程中，我们有点像一个人试图理解一块封闭的手表的机制。他看到了表盘和转动的指针，甚至听到了它的滴答声，但他却无法打开表壳。如果他聪明的话，他可能会形成某种机制的图景，这种机制可以解释他所观察到的所有事物，但他可能永远无法完全确定他的图景是唯一可以解释他所观察到的事物的图景。他永远无法将他的图景与真实的机制进行比较，他甚至无法想象这种比较的可能性或意义。但他肯定相信，随着知识的增加，他对现实的图景将变得越来越简单，并将解释他越来越广泛的感官印象。

Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world. In our endeavour to understand reality we are somewhat like a man trying to understand the mechanism o f a closed watch. He sees the face and the moving hands, even hears its ticking, but he has no way of opening the case. I f he is ingenious he may form some picture of a mechanism which could be responsible for all the things he observes, but he may never be quite sure his picture is the only one which could explain his observations. H e will never be able to compare his picture with the real mechanism and he cannot even imagine the possibility or the meaning of such a comparison. But he certainly believes that, as his knowledge increases, his picture of reality will become simpler and simpler and will explain a wider and wider range o f his sensuous impressions.

他或许也相信知识存在着理想的极限，而且人类的思维可以接近这个极限，他或许把这个理想的极限称为客观真理。

He may also believe in the existence of the ideal limit of knowledge and that it is approached by the human mind. H e may call this ideal limit the objective truth.

电子工程

E E

三十四

ONEGLUEREMA 在 S

O N E G L U E R E M A IN S

初学力学时，人们会觉得这门科学的所有方面都很简单、基本、一劳永逸。人们几乎不会怀疑存在一条三百年来无人注意的重要线索。这条被忽视的线索与力学的基本概念之一—— 质量有关。

When first studying mechanics one has the impression that everything in this branch of science is simple, fundamental and settled for all time. One would hardly suspect the existence o f an important clue which no one noticed for three hundred years. The neglected clue is connected with one of the fundamental concepts o f mechanics— that of mass.

我们再回到在平坦道路上推车的简单理想化实验。如果车最初处于静止状态，然后受到推动，它随后会以一定的速度均匀移动。假设力的作用可以重复任意多次，推动机制以相同的方式作用并在同一辆车上施加相同的力。无论实验重复多少次，最终速度始终相同。但如果实验改变，如果之前车是空的，现在装满了东西，会发生什么情况？满载的车的最终速度将小于空车。结论是：如果相同的力作用于两个不同的物体，最初都处于静止状态，则产生的速度将不同。我们说速度取决于物体的质量，质量越大，速度越小。

Again we return to the simple idealized experiment of the cart on a perfectly smooth road. I f the cart is initially at rest and then given a push, it afterwards moves uniformly with a certain velocity. Suppose that the action of the force can be repeated as many times as desired, the mechanism of pushing acting in the same way and exerting the same force on the same cart. However many times the experiment is repeated, the final velocity is always the same. But what happens if the experiment is changed, if previously the cart was empty and now it is loaded? The loaded cart will have a smaller final velocity than the empty one. The conclusion is: if the same force acts on two different bodies, both initially at rest, the resulting velocities will not be the same. We say that the velocity depends on the mass o f the body, being smaller if the mass is greater.

因此，我们至少在理论上知道如何确定物体的质量，或者更确切地说，一个物体的质量比另一个物体大多少倍。我们有相同的力作用在两个静止物体上。发现

We know, therefore, at least in theory, how to determine the mass o f a body or, more exactly, how many times greater one mass is than another. We have identical forces acting on two resting masses. Finding

三十五

第一个质量的速度是第二个质量的三倍，我们得出结论，第一个质量比第二个质量小三倍。这当然不是一种确定两个质量比率的实用方法。然而，我们可以想象用这种方法或类似的方法，基于惯性定律的应用来做到这一点。

that the velocity of the first mass is three times greater than that of the second, we conclude that the first mass is three times smaller than the second. This is certainly not a very practical way of determining the ratio of two masses. We can, nevertheless, well imagine having done it in this, or in some similar way, based upon the application of the law of inertia.

在实践中我们究竟如何确定质量？当然不是用刚才描述的方法。每个人都知道正确答案。我们通过称重来做到这一点。

How do we really determine mass in practice? Not, of course, in the way just described. Everyone knows the correct answer. We do it by weighing on a scale.

让我们更详细地讨论确定质量的两种不同方法。

Let us discuss in more detail the two different ways of determining mass.

第一个实验与重力（地球的吸引力）毫无关系。推车在被推后沿着一个完全光滑的水平面移动。使车停在平面上的重力不会改变，也不会对质量的测定产生任何影响。称重则完全不同。如果地球不吸引物体，如果重力不存在，我们就永远无法使用秤。

The first experiment had nothing whatever to do with gravity, the attraction of the earth. The cart moves along a perfectly smooth and horizontal plane after the push. Gravitational force, which causes the cart to stay on the plane, does not change, and plays no role in the determination of the mass. It is quite different with weighing. We could never use a scale if the earth did not attract bodies, if gravity did not exist.

两种质量测定方法的区别在于，第一种与引力无关，而第二种则本质上基于引力的存在。

The difference between the two determinations o f mass is that the first has nothing to do with the force of gravity while the second is based essentially on its existence.

我们要问：如果用上述两种方法分别测定两个质量的比值，得到的结果是否一样呢？实验给出的答案是十分清楚的。

We ask: if we determine the ratio of two masses in both ways described above, do we obtain the same result? The answer given by experiment is quite clear.

结果完全一样！这个结论是无法预见的，它是基于观察，而不是推理。为了简单起见，我们称

The results are exactly the same! This conclusion could not have been foreseen, and is based on observation, not reason. Let us, for the sake of simplicity, call the

三十六

按第一种方式决定的质量是 惯性质量 ，按第二种方式决定的质量是引力质量。在我们的世界中，它们恰好相等，但是我们完全可以想象，情况根本不应该如此。另一个问题随之而来：这两种质量的同一性纯属偶然，还是有更深层的意义？从古典物理学的角度来看，答案是：两种质量的同一性是偶然的，不应赋予它更深层的意义。现代物理学的答案恰恰相反：两种质量的同一性是根本性的，是一条新的、必不可少的线索，可引导我们获得更深刻的理解。事实上，这是所谓广义相对论得以发展的最重要线索之一。

mass determined in the first way the inertial mass and that determined in the second way the gravitational mass. In our world it happens that they are equal, but we can well imagine that this should not have been the case at all. Another question arises immediately: is this identity of the two kinds o f mass purely accidental, or does it have a deeper significance? The answer, from the point o f view o f classical physics, is: the identity of the two masses is accidental and no deeper significance should be attached to it. The answer of modern physics is just the opposite: the identity of the two masses is fundamental and forms a new and essential clue leading to a more profound understanding. This was, in fact, one of the most important clues from which the so-called general theory o f relativity was developed.

如果一部悬疑小说将奇异事件解释为意外，那么它似乎就低劣了。让故事遵循合理的模式当然更令人满意。同样，一种解释引力和惯性质量同一性的理论优于一种将其同一性解释为意外的理论，当然，前提是这两种理论与观察到的事实同样一致。

A mystery story seems inferior if it explains strange events as accidents. It is certainly more satisfying to have the story follow a rational pattern. In exactly the same way a theory which offers an explanation for the identity o f gravitational and inertial mass is superior to one which interprets their identity as accidental, provided, o f course, that the two theories are equally consistent with observed facts.

由于惯性质量和引力质量的这种同一性是相对论的基础，因此我们有必要在此更仔细地研究它。哪些实验可以令人信服地证明这两个质量相同？答案就在伽利略的旧实验中，在该实验中，他从塔上扔下不同的质量。他注意到，从塔上扔下所需的时间

Since this identity o f inertial and gravitational mass was fundamental for the formulation of the theory of relativity, we are justified in examining it a little more closely here. What experiments prove convincingly that the two masses are the same? The answer lies in Galileo’s old experiment in which he dropped different masses from a tower. H e noticed that the time required

三十七

因为坠落总是相同的，即坠落物体的运动不依赖于质量。要将这个简单但非常重要的实验结果与两个质量的同一性联系起来，需要一些相当复杂的推理。

for the fall was always the same, that the motion of a falling body does not depend on the mass. T o link this simple but highly important experimental result with the identity of the two masses needs some rather intricate reasoning.

静止的物体在外力作用下会屈服，运动并达到一定的速度。物体屈服的难易程度取决于其惯性质量，质量大时抵抗运动的能力强于质量小时。我们可以毫不夸张地说：物体对外力的响应程度取决于其惯性质量。如果地球以相同的力吸引所有物体，那么惯性质量最大的物体下落的速度会比其他物体慢。但事实并非如此：所有物体下落的方式都一样。

A body at rest gives way before the action of an external force, moving and attaining a certain velocity. It yields more or less easily, according to its inertial mass, resisting the motion more strongly if the mass is large than if it is small. We may say, without pretending to be rigorous: the readiness with which a body responds to the call of an external force depends on its inertial mass. I f it were true that the earth attracts all bodies with the same force, that of greatest inertial mass would move more slowly in falling than any other. But this is not the case: all bodies fall in the same way.

这意味着地球吸引不同质量物体的力一定不同。现在地球用重力吸引石头，而对石头的惯性质量一无所知。地球的“召唤”力取决于重力质量。石头的“回应”运动取决于惯性质量。由于“回应”运动始终相同

This means that the force by which the earth attracts different masses must be different. Now the earth attracts a stone with the force of gravity and knows nothing about its inertial mass. The “ calling” force of the earth depends on the gravitational mass. The “ answering” motion of the stone depends on the inertial mass. Since the “ answering ” motion is always the same

— 从相同高度落下的所有物体都以相同的方式下落——必须推断引力质量和惯性质量相等。

— all bodies dropped from the same height fall in the same way— it must be deduced that gravitational mass and inertial mass are equal.

一位物理学家更迂腐地提出了同样的结论：落体加速度与其引力质量成正比增加，与其惯性质量成正比减少。因为所有落体

More pedantically a physicist formulates the same conclusion: the acceleration of a falling body increases in proportion to its gravitational mass and decreases in proportion to its inertial mass. Since all falling bodies

三十八

具有相同的恒定加速度，两个质量必定相等。

have the same constant acceleration, the two masses must be equal.

在我们伟大的神秘故事中，没有一个问题可以永远得到彻底解决和解决。三百年后，我们不得不回到最初的运动问题，修改调查程序，寻找被忽视的线索，从而对周围的宇宙有了不同的认识。

In our great mystery story there are no problems wholly solved and settled for all time. After three hundred years we had to return to the initial problem of motion, to revise the procedure o f investigation, to find clues which had been overlooked, thereby reaching a different picture of the surrounding universe.

热是一种物质吗

IS H E A T A S U B S T A N C E

在这里我们开始追寻一条新线索，这条线索源自热现象领域。然而，将科学划分为独立且不相关的部分是不可能的。

Here we begin to follow a new clue, one originating in the realm of heat phenomena. It is impossible, however, to divide science into separate and unrelated sections.

事实上，我们很快就会发现，这里介绍的新概念与那些我们已经熟悉的概念以及我们将继续遇到的概念交织在一起。在一门科学中发展起来的思路通常可以应用于描述性质显然完全不同的事件。在这个过程中，原始概念经常被修改，以便促进对它们起源的现象和它们新应用的现象的理解。

Indeed, we shall soon find that the new concepts introduced here are interwoven with those already familiar, and with those we shall still meet. A line of thought developed in one branch of science can very often be applied to the description o f events apparently quite different in character. In this process the original concepts are often modified so as to advance the understanding both o f those phenomena from which they sprang and of those to which they are newly applied.

描述热现象的最基本概念是温度和热量。在科学史上，区分这两者花了令人难以置信的漫长时间，但一旦做出区分，就会取得快速进展。虽然这些概念现在已为大家所熟悉，但我们将仔细研究它们，强调它们之间的差异。

The most fundamental concepts in the description of heat phenomena are temperature and heat. It took an unbelievably long time in the history of science for these two to be distinguished, but once this distinction was made rapid progress resulted. Although these concepts are now familiar to everyone, we shall examine them closely, emphasizing the differences between them.

我们的触觉可以非常明确地告诉我们，一个物体是热的，另一个是冷的。但这只是一种纯粹的定性标准，不足以进行定量描述，有时甚至含糊不清。一个著名的实验证明了这一点：我们有三个容器，分别装有冷水、热水和热水。如果我们将一只手伸进冷水，另一只手伸进热水，我们会从第一只手那里得到天气冷的信息，从第二只手那里得到天气热的信息。如果我们将两只手都伸进同样的温水中，我们会从每只手那里得到两个相互矛盾的信息。出于同样的原因，一个爱斯基摩人和某个赤道国家的土著人在春天在纽约会面时，对气候是热还是冷有不同的看法。我们用温度计来解决所有这些问题，温度计是伽利略设计的一种原始仪器。这里又出现了那个熟悉的名字！温度计的使用基于一些明显的物理假设。我们将通过引用大约一百五十年前布莱克在演讲中的几句话来回顾它们，布莱克对澄清与热和温度这两个概念有关的困难做出了巨大贡献：

O ur sense of touch tells us quite definitely that one body is hot and another cold. But this is a purely qualitative criterion, not sufficient for a quantitative description and sometimes even ambiguous. This is shown by a well-known experiment: we have three vessels containing, respectively, cold, warm and hot water. I f we dip one hand into the cold water and the other into the hot, we receive a message from the first that it is cold and from the second that it is hot. I f we then dip both hands into the same warm water, we receive two contradictory messages, one from each hand. For the same reason an Eskimo and a native o f some equatorial country meeting in New York on a spring day would hold different opinions as to whether the climate was hot or cold. We settle all such questions by the use o f a thermometer, an instrument designed in a primitive form by Galileo. Here again that familiar name ! The use o f a thermometer is based on some obvious physical assumptions. We shall recall them by quoting a few lines from lectures given about a hundred and fifty years ago by Black, who contributed a great deal toward clearing up the difficulties connected with the two concepts, heat and temperature:

通过使用这个仪器，我们了解到，如果我们取 1000 种或更多种不同的物质，例如金属、石头、盐、木材、羽毛、羊毛、水和各种其他液体，尽管它们一开始的温度都不同，但把它们放在同一个没有火的房间里，太阳也不会照进来，热量就会从较热的物体传递到较冷的物体，也许在几个小时内，或者在一天的时间里，

By the use of this instrument we have learned, that if we take 1000, or more, different kinds of matter, such as metals, stones, salts, woods, feathers, wool, water and a variety of other fluids, although they be all at first of different heats, let them be placed together in the same room without a fire, and into which the sun does not shine, the heat will be communicated from the hotter of these bodies to the colder, during some hours perhaps, or the course of a day ,

在这段时间结束时，如果我们用温度计依次测量它们，它将精确地指向相同的温度。

at the end of which time, if we apply a thermometer to them all in succession, it will point precisely to the same degree.

根据现今的命名法，斜体字“ heats”应该被“ temperatures”取代。

The italicized word heats should, according to present-day nomenclature, be replaced by the word temperatures.

医生从病人嘴里取出温度计时，可能会这样推理：“温度计通过水银柱的长度来指示自己的温度。我们假设水银柱的长度与温度的升高成正比。但是温度计与我的病人接触了几分钟，因此病人和温度计的温度相同。因此，我得出结论，病人的体温就是温度计上显示的体温。”医生的行为可能是机械的，但他不假思索地运用了物理原理。

A physician taking the thermometer from a sick man’s mouth might reason like this: “ The thermometer indicates its own temperature by the length of its column of mercury. We assume that the length o f the mercury column increases in proportion to the increase in temperature. But the thermometer was for a few minutes in contact with my patient, so that both p atient and thermometer have the s ame temperature. I conclude, therefore, that my patient’s temperature is that registered on the thermometer.” The doctor probably acts mechanically, but he applies physical principles without thinking about it.

但温度计含有的热量和人体的热量一样吗？当然不是。如果仅仅因为两个物体的温度相等就认为它们含有等量的热量，正如布莱克所说，

But does the thermometer contain the same amount of heat as the body o f the man? O f course not. To assume that two bodies contain equal quantities of heat just because their temperatures are equal would, as Black remarked, be

对这个问题的看法过于草率。它混淆了不同物体的热量和其一般强度或强度，尽管很明显，这是两个不同的东西，当我们考虑热量的分布时，应该始终加以区分。

taking a very hasty view of the subject. It is confounding the quantity of heat in different bodies with its general strength or intensity, though it is plain that these are two different things, and should always be distinguished, when we are thinking of the distribution of heat.

我们可以通过一个非常简单的实验来理解这种区别。一磅

A n understanding of this distinction can be gained by considering a very simple experiment. A pound of

置于燃气火焰上的水需要一些时间才能从室温变为沸点。

water placed over a gas flame takes some time to change from room temperature to the boiling point.

用同样的火焰加热同一容器中的 12 磅水需要更长的时间。我们将这一事实解释为现在需要更多的“某种东西”，我们称之为

A much longer time is required for heating twelve pounds, say, of water in the same vessel by means of the same flame. We interpret this fact as indicating that now more o f “ something” is needed and we call this

“ 某物 ” 热。

“ something” heat.

另一个重要概念， 即比热， 是通过以下实验获得的：让一个容器中装有一磅水，另一个容器中装有一磅水银，以同样的方式加热两者。水银比水热得快得多，这表明水银比水热得慢。

A further important concept, specific heat, is gained by the following experiment: let one vessel contain a pound o f water and another a pound o f mercury, both to be heated in the same way. The mercury gets hot much more quickly than the water, showing that less

要使温度升高一度，就需要“热量”。

“ heat” is needed to raise the temperature by one degree.

一般来说，需要不同量的“热量”才能将不同物质（如水、水银、铁、铜、木材等）的温度改变一度，例如从 40 华氏度变为 41 华氏度，这些物质的质量相同。我们说每种物质都有各自的热容量 或 比热。

In general, different amounts o f “ heat” are required to change by one degree, say from 40 to 41 degrees Fahrenheit, the temperatures o f different substances such as water, mercury, iron, copper, wood, etc., all of the same m ass. We say that each substance has its individual heat capacity, or specific heat.

一旦掌握了热的概念，我们就可以更深入地研究它的性质。我们有两个物体，一个是热的，另一个是冷的，或者更准确地说，一个的温度比另一个高。我们让它们接触，并让它们不受所有其他外部影响。我们知道，最终它们会达到相同的温度。但这是如何发生的？从它们接触到达到相同温度之间会发生什么？

Once having gained the concept of heat, we can investigate its nature more closely. We have two bodies, one hot, the other cold, or more precisely, one o f a higher temperature than the other. We bring them into contact and free them from all other external influences. Eventually they will, we know, reach the same temperature. But how does this take place? What happens between the instant they are brought into contact and the achievement of equal temperatures?

热量从一个物体“流动”到另一个物体的画面清晰可见，就像水从较高的

The picture of heat “ flowing” from one body to another suggests itself, like water flowing from a higher

四十二

水平下降。这幅图虽然原始，但似乎符合许多事实，因此类比如下：水——热

level to a lower. This picture, though primitive, seems to fit many of the facts, so that the analogy runs: Water— Heat

更高水平—更高温度

Higher level— Higher temperature

较低水平—较低温度

Lower level— Lower temperature

流动一直持续到两个水平（即两个温度）相等为止。定量考虑可以使这种天真的观点更加有用。如果将一定质量的水和酒精（每种都处于一定温度）混合在一起，则了解比热容将有助于预测混合物的最终温度。相反，观察最终温度，再加上一点代数运算，我们就可以找到两个比热容的比率。

The flow proceeds until both levels, that is, both temperatures, are equal. This naïve view can be made more useful by quantitative considerations. I f definite masses o f water and alcohol, each at a definite temperature, are mixed together, a knowledge o f the specific heats will lead to a prediction o f the final temperature o f the mixture. Conversely, an observation o f the final temperature, together with a little algebra, would enable us to find the ratio of the two specific heats.

我们在这里看到的热概念与其他物理概念有相似之处。根据我们的观点，热是一种物质，如力学中的质量。它的数量可能会改变，也可能不会改变，就像放在保险箱里的钱或花掉的钱一样。只要保险箱保持锁定状态，保险箱里的钱数就会保持不变，孤立物体中的质量和热量也是如此。理想的热水瓶类似于这样的保险箱。此外，正如孤立系统的质量即使发生化学变化也不会改变一样，热量即使从一个物体流向另一个物体也会守恒。即使热量不是用来提高物体的温度，而是用来融化冰，或者把水变成蒸汽，我们仍然可以把它看作是一种物质，并通过

We recognize in the concept of heat which appears here a similarity to other physical concepts. H eat is, according to our view, a substance, such as mass in mechanics. Its quantity may change or not, like money put aside in a safe or spent. The amount o f money in a safe will remain unchanged so long as the safe remains locked, and so will the amounts of mass and heat in an isolated body. The ideal thermos flask is analogous to such a safe. Furthermore, just as the mass of an isolated system is unchanged even if a chemical transformation takes place, so heat is conserved even though it flows from one body to another. Even if heat is not used for raising the temperature o f a body but for melting ice, say, or changing water into steam, we can still think o f it as a substance and regain it entirely by

冻结水或液化蒸汽。旧名称“熔化潜热”或“汽化潜热”表明这些概念源自热作为一种物质的图景。潜热暂时被隐藏，就像放在保险箱里的钱一样，但如果知道锁的密码，就可以使用。

freezing the water or liquefying the steam. The old names, latent heat o f melting or vaporization, show that these concepts are drawn from the picture of heat as a substance. Latent heat is temporarily hidden, like money put away in a safe, but available for use if one knows the lock combination.

但热肯定不是与质量相同意义上的物质。质量可以用秤来测量，但热呢？一块铁在炽热时比在冰冷时重吗？实验表明并非如此。如果热是一种物质，它就是无重量的。“热物质”通常被称为 热量物质，这是我们在整个无重量物质家族中第一次认识的物质。稍后我们将有机会追溯这个家族的历史，它的兴衰。现在只需注意这个特定成员的诞生就足够了。

But heat is certainly not a substance in the same sense as mass. Mass can be detected by means of scales, but what of heat? Does a piece of iron weigh more when red-hot than when ice-cold? Experiment shows that it does not. I f heat is a substance at all, it is a weightless one. The “ heat-substance” was usually called caloric and is our first acquaintance among a whole family of weightless substances. Later we shall have occasion to follow the history of the family, its rise and fall. It is sufficient now to note the birth of this particular member.

任何物理理论的目的都是解释尽可能广泛的现象。只要它确实使事件变得可以理解，它就是合理的。我们已经看到，物质理论解释了许多热现象。然而，很快就会发现，这又是一个错误的线索，热不能被视为一种物质，即使是无重量的。如果我们思考一些标志着文明开始的简单实验，这一点就很清楚了。

The purpose of any physical theory is to explain as wide a range of phenomena as possible. It is justified in so far as it does make events understandable. We have seen that the substance theory explains many of the heat phenomena. It will soon become apparent, however, that this again is a false clue, that heat cannot be regarded as a substance, even weightless. This is clear if we think about some simple experiments which marked the beginning of civilization.

我们认为物质既不能被创造也不能被毁灭。然而，原始人通过摩擦创造了足够的热量来点燃木头。事实上，摩擦加热的例子有：

We think of a substance as something which can be neither created nor destroyed. Yet primitive man created by friction sufficient heat to ignite wood. Examples of heating by friction are, as a matter of fact,

四十四

太多了，太熟悉了，不需要再叙述。

much too numerous and familiar to need recounting.

在所有这些情况下，都会产生一定量的热量，这是物质理论难以解释的一个事实。当然，该理论的支持者可以发明论据来解释这一点。他的理由大致如下：“物质理论可以解释热量的明显产生。举个最简单的例子，两块木头互相摩擦。摩擦会影响木材并改变其性质。很可能这些性质发生了改变，以至于热量不变却产生了比以前更高的温度。毕竟，我们唯一注意到的就是温度的上升。摩擦可能改变了木材的比热，而不是总热量。”

In all these cases some quantity of heat is created, a fact difficult to account for by the substance theory. It is true that a supporter of this theory could invent arguments to account for it. His reasoning would run something like this: “ The substance theory can explain the apparent creation o f heat. Take the simplest example o f two pieces o f wood rubbed one against the other. Now rubbing is something which influences the wood and changes its properties. It is very likely that the properties are so modified that an unchanged quantity of heat comes to produce a higher temperature than before. After all, the only thing we notice is the rise in temperature. It is possible that the friction changes the specific heat of the wood and not the total amount of heat.”

在讨论的这个阶段，与实体理论的支持者争论是毫无意义的，因为这个问题只有通过实验才能解决。

A t this stage o f the discussion it would be useless to argue with a supporter o f the substance theory, for this is a matter which can be settled only by experiment.

想象两块相同的木头，假设相同的温度变化是由不同的方法引起的；例如，一种是通过摩擦，另一种是通过与散热器接触。如果这两块木头在新的温度下具有相同的比热，那么整个物质理论就必须崩溃。确定比热的方法非常简单，理论的命运取决于这些测量的结果。能够对理论的生死做出裁决的测试在物理学史上经常出现，被称为 关键测试

Imagine two identical pieces of wood and suppose equal changes o f temperature are induced by different methods; in one case by friction and in the other by contact with a radiator, for example. I f the two pieces have the same specific heat at the new temperature, the whole substance theory must break down. There are very simple methods for determining specific heats, and the fate o f the theory depends on the result of just such measurements. Tests which are capable of pronouncing a verdict of life or death on a theory occur frequently in the history o f physics, and are called crucial

四十五

实验。实验的关键价值只有通过问题的提出方式才能揭示出来，而且只有一种现象理论可以通过实验来检验。确定两个相同物体在通过摩擦和热流分别达到相同温度时的比热，就是关键实验的典型例子。这项实验大约一百五十年前由朗福德进行，对物质热理论造成了致命一击。

experiments. The crucial value of an experiment is revealed only by the way the question is formulated, and only one theory of the phenomena can be put on trial by it. The determination of the specific heats of two bodies of the same kind, at equal temperatures attained by friction and heat flow respectively, is a typical example of a crucial experiment. This experiment was performed about a hundred and fifty years ago by Rumford, and dealt a death blow to the substance theory o f heat.

朗福德本人的一段叙述讲述了这样一个故事：

A n extract from Rumford’s own account tells the story:

在日常生活中，经常会出现这样的机会：思考大自然的一些最奇妙的运作方式；而且，利用仅为艺术和制造的机械目的而设计的机器，常常可以进行非常有趣的哲学实验，而且几乎不费吹灰之力。

It frequently happens, that in the ordinary affairs and occupations of life, opportunities present themselves of contemplating some of the most curious operations of Nature; and very interesting philosophical experiments might often be made, almost without trouble or expense, by means of machinery contrived for the mere mechanical purposes of the arts and manufactures.

我常常有这样的观察，并且坚信，养成密切关注日常生活中发生的一切事情的习惯，往往会在偶然中或在想象力的游玩中，通过思考最常见的现象，产生有用的怀疑，并制定合理的调查和改进计划，而这些效果比哲学家们在专门安排用于学习的时间里进行的更深入的沉思更有效。...

I have frequently had occasion to make this observation; and am persuaded, that a habit of keeping the eyes open to every thing that is going on in the ordinary course of the business of life has oft ener led, as it were by accident, or in the playful excursions of the imagination, put into action by contemplating the most common appearances, to useful doubts, and sensible schemes for investigation and improvement, than all the more intense meditations of philosophers, in the hours expressly set apart for study. . . .

最近，我在慕尼黑军工厂的车间里负责大炮的钻孔工作，我惊讶地发现，黄铜枪在钻孔过程中，在很短的时间内会产生很大的热量；而且，这种热量还要强烈得多（比

Being engaged, lately, in superintending the boring of cannon, in the workshops of the military arsenal at Munich, I was struck with the very considerable degree of Heat which a brass gun acquires, in a short time, in being bored; and with the still more intense Heat (much greater than

四十六

我通过实验发现，钻孔机从中分离出的金属碎片的体积与沸水的体积相当。

that of boiling water, as I found by experiment) of the metallic chips separated from it by the borer.. . .

上述机械运转中实际产生的热量是从哪里来的呢？

From whence comes the Heat actually produced in the mechanical operation above mentioned?

它是由钻机从金属固体中分离出来的金属碎片提供的吗？

Is it furnished by the metallic chips which are separated by the borer from the solid mass of metal?

如果是这样的话，那么根据现代潜热和热能理论，容量不仅应该改变，而且它们所经历的变化应该足够大以解释产生的所有热量。

I f this were the case, then, according to the modern doctrines of latent Heat, and of caloric, the capacity ought not only to be changed, but the change undergone by them should be sufficiently great to account for all the Heat produced.

但并没有发生这样的变化；因为我发现，取等量（按重量）的碎片和用细锯切开的同一块金属的薄片，并在相同温度（沸水的温度）下将它们放入等量的冷水中（即温度为 59½°F），放入碎片的那部分水看起来并没有比放入金属片的另一部分水加热得更热或更热。

But no such change had taken place; for I found, upon taking equal quantities, by weight, of these chips, and of thin slips of the same block of metal separated by means of a fine saw and putting them, at the same temperature (that of boiling water), into equal quantities of cold water (that is to say, at the temperature of 59½ ° F.) the portion of water into which the chips were put was not, to all appearance, heated either less or more than the other portion, in which the slips of metal were put.

最后我们得出他的结论：

Finally we reach his conclusion:

并且，在对这个问题进行推理时，我们不能忘记考虑最显著的情况，即在这些实验中，摩擦产生的热量的来源显然是取之不尽的。

And, in reasoning on this subject, we must not forget to consider that most remarkable circumstance, that the source of the Heat generated by friction, in these Experiments, appeared evidently to be inexhaustible.

几乎没有必要补充，任何绝缘体 或物体系统能够不受限制地继续提供的任何东西都不可能成为物质；在我看来，要形成任何能够被激发和传递的东西的独特概念是极其困难的，如果不是完全不可能的话，就像这些实验中热量被激发和传递的方式一样，除非它是 运动。

It is hardly necessary to add, that anything which any insulated body, or system of bodies, can continue to furnish without limitation, cannot possibly be a material substance; and it appears to me to be extremely difficult, if not quite impossible, to form any distinct idea of anything, capable of being excited and communicated, in the manner the Heat was excited and communicated in these Experiments, except i t be m o t i o n .

因此，我们看到旧理论的崩溃，或者更确切地说，我们看到实体理论

Thus we see the breakdown of the old theory, or to be more exact, we see that the substance theory is

四十七

仅限于热流问题。同样，正如朗福德所暗示的那样，我们必须寻找新的线索。为此，让我们暂时放下热问题，回到力学上。

limited to problems of heat flow. Again, as Rumford has intimated, we must seek a new clue. To do this, let us leave for the moment the problem of heat and return to mechanics.

THESW IT回拨

T H E S W IT C H B A C K

让我们来追踪一下广受欢迎的惊险刺激之字形弯道的运动。一辆小车被举起或开到轨道的最高点。当它被释放时，它在重力的作用下开始向下滚动，然后沿着一条奇妙的曲线上下移动，速度的突然变化让乘客感到惊险刺激。

Let us trace the motion of that popular thrill-giver, the switchback. A small car is lifted or driven to the highest point of the track. When set free it starts rolling down under the force of gravity, and then goes up and down along a fantastically curved line, giving the occupants a thrill by the sudden changes in velocity.

每一个折返运动都有它的最高点，也就是它开始的地方。在整个运动过程中，它永远不会再达到相同的高度。对运动的完整描述将非常复杂。

Every switchback has its highest point, that from which it starts. Never again, throughout the whole course of the motion, will it reach the same height. A complete description of the motion would be very complicated.

一方面是问题的机械方面，即速度和位置随时间的变化。另一方面是摩擦，因此在轨道和车轮中产生热量。将物理过程分为这两个方面的唯一重要原因是为了能够使用前面讨论过的概念。这种划分导致了理想化的实验，因为只出现机械方面的物理过程只能想象而永远无法实现。

O n the one hand is the mechanical side of the problem, the changes of velocity and position in time. O n the other there is friction and therefore the creation of heat, on the rail and in the wheels. The only significant reason for dividing the physical process into these two aspects is to make possible the use of the concepts previously discussed. The division leads to an idealized experiment, for a physical process in which only the mechanical aspect appears can be only imagined but never realized.

对于理想化的实验，我们可以想象有人已经学会了完全消除运动中始终伴随的摩擦力。他决定将他的发现应用于折返道的建造，并且

For the idealized experiment we may imagine that someone has learned to eliminate entirely the friction which always accompanies motion. H e decides to apply his discovery to the construction of a switchback, and

四十八

必须自己找出如何建造一条轨道的方法。汽车要上下行驶，其起点位于地面以上一百英尺。他很快通过反复试验发现，他必须遵循一个非常简单的规则：他可以按照自己喜欢的任何路径建造轨道，只要没有一个点高于起点即可。如果汽车要自由行驶到赛道的终点，它的高度可以达到一百英尺，但不能超过这个高度。由于摩擦力，实际轨道上的汽车永远无法达到初始高度，但我们假设的工程师不需要考虑这一点。

must find out for himself how to build one. The car is to run up and down, with its starting-point, say, at one hundred feet above ground level. H e soon discovers by trial and error that he must follow a very simple rule: he may build his track in whatever path he pleases so long as no point is higher than the starting-point. I f the car is to proceed freely to the end o f the course, its height may attain a hundred feet as many times as he likes, but never exceed it. The initial height can never be reached by a car on an actual track because of friction, but our hypothetical engineer need not consider that.

让我们跟随理想化的汽车在理想化的之字形道路上的运动，当它从起点开始向下滚动时。随着它移动，它与地面的距离减小，但速度增加。乍一看，这句话可能让我们想起了语言课上的一句话：“我没有铅笔，但你有六个橘子。”然而，它并没有那么愚蠢。我没有铅笔和你有六个橘子之间没有联系，但存在着非常真实的相关性

Let us follow the motion of the idealized car on the idealized switchback as it begins to roll downward from the starting-point. As it moves its distance from the ground diminishes, but its speed increases. This sentence at first sight may remind us o f one from a language lesson: “ I have no pencil, but you have six oranges.” It is not so stupid, however. There is no connection between my having no pencil and your having six oranges, but there is a very real correlation

汽车与地面的距离和其速度之间的关系。如果我们知道汽车与地面之间的高度，我们就可以随时计算出汽车的速度，但我们在这里省略了这一点，因为它的定量特性可以用数学公式来最好地表达。

between the distance o f the car from the ground and its speed. We can calculate the speed of the car at any moment if we know how high it happens to be above the ground, but we omit this point here because o f its quantitative character which can best be expressed by mathematical formulae.

在最高点，汽车速度为零，距地面一百英尺。在最低点，汽车与地面没有距离，速度最大。这些事实也可以用其他术语来表达。在最高点，汽车有势能，没有动能或运动能。在最低点，汽车动能最大，没有势能。在所有中间位置，只要有一定速度和高度，汽车就同时具有动能和势能。势能随着高度的增加而增加，而动能随着速度的增加而增大。力学原理足以解释这种运动。

A t its highest point the car has zero velocity and is one hundred feet from the ground. A t the lowest possible point it is no distance from the ground, and has its greatest velocity. These facts may be expressed in other terms. A t its highest point the car has potential energy but no kinetic energy or energy o f motion. A t its lowest point it has the greatest kinetic energy and no potential energy whatever. A t all intermediate positions, where there is some velocity and some elevation, it has both kinetic and potential energy. The potential energy increases with the elevation, while the kinetic energy becomes greater as the velocity increases. The principles of mechanics suffice to explain the motion.

在数学描述中，能量有两种表达方式，虽然总和不变，但每种方式都会发生变化。因此，可以从数学上严格地引入势能（取决于位置）和动能（取决于速度）的概念。当然，引入这两个名称是任意的，只是为了方便。

Two expressions for energy occur in the mathematical description, each of which changes, although the sum does not vary. It is thus possible to introduce mathematically and rigorously the concepts of potential energy, depending on position, and kinetic energy, depending on velocity. The introduction of the two names is, of course, arbitrary and justified only by convenience.

两个量的总和保持不变，称为运动常数。总能量（动能加上势能）可以比作金额保持不变但变化的货币

The sum of the two quantities remains unchanged, and is called a constant of the motion. The total energy, kinetic plus potential, can be compared, for example, with money kept intact as to amount but changed

持续来自，一个 curr 5

continually from, one curr 5

ency 到另一个，比如说从

ency to another, say from

按照明确的汇率将美元兑换成英镑，然后再兑换回美元。

dollars to pounds and back again, according to a well-defined rate of exchange.

在真实的折返弯道中，摩擦力会阻止汽车再次达到与出发时一样高的高度，此时动能和势能之间仍会不断变化。然而，此时总和并不保持不变，而是会变得越来越小。

In the real switchback, where friction prevents the car from again reaching as high a point as that from which it started, there is still a continuous change between kinetic and potential energy. Here, however, the sum does not remain constant, but grows smaller.

现在需要迈出重要而勇敢的一步，将运动的机械方面和热方面联系起来。

Now one important and courageous step more is needed to relate the mechanical and heat aspects of motion.

此步骤的丰富后果和概括将在后面看到。

The wealth of consequences and generalizations from this step will be seen later.

现在涉及到的不仅仅是动能和势能，即摩擦产生的热量。

Something more than kinetic and potential energies is now involved, namely, the heat created by friction.

这种热量是否对应于机械能（即动能和势能）的减少？

Does this heat correspond to the diminution in mechanical energy, that is kinetic and potential energy?

一个新的猜测即将出现。如果热量可以被视为一种能量形式，那么热量、动能和势能的总和可能保持不变。不仅仅是热量，还有热量和其他形式的能量

A new guess is imminent. I f heat may be regarded as a form o f energy, perhaps the sum of all three— heat, kinetic and potential energies— remains constant. Not heat alone, but heat and other forms of energy taken

就像物质 5

together are, like a substan 5

ce，坚不可摧。就好像

ce, indestructible. It is as if

一个人将美元兑换成英镑时必须向自己支付法郎的佣金，这笔佣金也被节省下来，这样美元、英镑和法郎的总额就成为一个固定的金额，按照某个确定的汇率。

a man must pay himself a commission in francs for changing dollars to pounds, the commission money also being saved so that the sum o f dollars, pounds, and francs is a fixed amount according to some definite exchange rate.

科学的进步已经摧毁了热作为一种物质的旧观念。我们试图创造一种新的物质，即能量，热是其形式之一。

The progress of science has destroyed the older concept o f heat as a substance. We try to create a new substance, energy, with heat as one o f its forms.

汇率

T H E R A T E O F E X C H A N G E

不到一百年前，迈耶猜测到了导致热是一种能量的新线索，而焦耳通过实验证实了这一线索。奇怪的是，几乎所有与热的性质有关的基础工作都是由非专业物理学家完成的，他们只是把物理当作自己的业余爱好。他们当中有多才多艺的苏格兰人布莱克、德国医生迈耶和伟大的美国冒险家朗福德伯爵，朗福德伯爵后来住在欧洲，并担任巴伐利亚战争部长等职务。还有英国酿酒师焦耳，他在业余时间进行了一些关于能量守恒的最重要的实验。

Less than a hundred years ago the new clue which led to the concept o f heat as a form of energy was guessed by Mayer and confirmed experimentally by Jou le. It is a strange coincidence that nearly all the fundamental work concerned with the nature of heat was done by non-professional physicists who regarded physics merely as their great hobby. There was the versatile Scotsman Black, the German physician Mayer, and the great American adventurer Count Rumford, who afterwards lived in Europe and, among other activities, became Minister of War for Bavaria. There was also the English brewer Joule who, in his spare time, performed some most important experiments concerning the conservation o f energy.

焦勒通过实验验证了热是能量的一种形式的猜测，并确定了交换速率。

Jou le verified by experiment the guess that heat is a form of energy, and determined the rate of exchange.

值得我们看看他的成果到底是什么。

It is worth our while to see just what his results were.

系统的动能和势能共同构成了系统的机械能。

The kinetic and potential energy of a system together constitute its mechanical energy. In the case of

在折返过程中，我们猜测部分机械能被转换成了热量。如果这是正确的，那么这里以及在所有其他类似的物理过程中，两者之间必定存在一定的 交换率 。这严格来说是一个定量问题，但一定量的机械能可以转化为一定量的热量这一事实非常重要。我们想知道什么数字表示交换率，即我们从一定量的机械能中获得多少热量。

the switchback we made a guess that some of the mechanical energy was converted into heat. I f this is right, there must be here and in all other similar physical processes a definite rate o f exchange between the two. This is rigorously a quantitative question, but the fact that a given quantity of mechanical energy can be changed into a definite amount of heat is highly important. We should like to know what number expresses the rate o f exchange, i.e., how much heat we obtain from a given amount of mechanical energy.

确定这个数字是焦耳的研究目标。他的一个实验的机制很像砝码钟的机制。这种钟的上弦包括提升两个砝码，从而为系统增加势能。如果不对钟进行进一步干扰，它可以看作是一个封闭系统。砝码逐渐下落，钟走时逐渐停止。在一定时间后，砝码将达到最低位置，钟停下。能量去哪儿了？砝码的势能转化为机制的动能，然后逐渐以热量的形式耗散。

The determination of this number was the object of Jo u le ’s researches. The mechanism of one o f his experiments is very much like that of a weight clock. The winding of such a clock consists o f elevating two weights, thereby adding potential energy to the system. I f the clock is not further interfered with, it may be regarded as a closed system. Gradually the weights fall and the clock runs down. A t the end of a certain time the weights will have reached their lowest position and the clock will have stopped. What has happened to the energy? The potential energy of the weights has changed into kinetic energy of the mechanism, and has then gradually been dissipated as heat.

这种机制的巧妙改造使焦耳能够测量热量损失，从而测量交换率。在他的装置中，两个重物使浸入水中的桨轮转动。重物的势能转化为可移动部件的动能，进而转化为热量，

A clever alteration in this sort of mechanism enabled Jou le to measure the heat lost and thus the rate of exchange. In his apparatus two weights caused a paddle wheel to turn while immersed in water. The potential energy of the weights was changed into kinetic energy of the movable parts, and thence into heat which

提高了水的温度。焦耳测量了这种温度变化，并利用已知的水的比热计算出吸收的热量。他总结了许多试验的结果如下：

raised the temperature o f the water. Jou le measured this change of temperature and, making use o f the known specific heat of water, calculated the amount of heat absorbed. H e summarized the results o f many trials as follows:

第一，无论是固体还是液体，物体摩擦产生的热量总是与所消耗的力（力焦耳表示能量）成正比。

1st. That the quantity of heat produced by the friction of bodies, whether solid or liquid, is always proportional to the quantity of force [by force Joule means energy] expended.

和

And

第二，要使一磅水（真空称重，温度在 55° 至 6o° 之间）的温度升高 1° 华氏度，需要消耗一定的机械力 [能量]

2nd. That the quantity of heat capable of increasing the temperature of a pound of water (weighed in vacuo and taken at between 55° and 6o°) by 1° Fahr. requires for its evolution the expenditure of a mechanical force [energy]

表示 772 磅的重量从一英尺的空间内坠落。

represented by the fall of 772 lb. through the space of one foot.

换句话说，离地面一英尺高 772 磅的势能相当于将一磅水的温度从 55°F 升高到 56°F 所需的热量。后来的实验者能够达到更高的精度，

In other words, the potential energy o f 772 pounds elevated one foot above the ground is equivalent to the quantity of heat necessary to raise the temperature o f one pound of water from 55° F . to 56° F . Later experimenters were capable o f somewhat greater accuracy,

但热的机械当量本质上正是焦勒在其开创性工作中所发现的。

but the mechanical equivalent o f heat is essentially what Jo u le found in his pioneer work.

这项重要工作完成后，进展很快。人们很快认识到，机械能和热能只是其众多形式中的两种。任何可以转化为其中任何一种的东西也是一种能量形式。太阳发出的辐射是能量，因为其中一部分在地球上转化为热量。电流具有能量，因为它加热电线或转动电动机的轮子。煤代表化学能，煤燃烧时释放为热量。在自然界中，每一种能量都会以某种明确的交换率转化为另一种能量。在一个封闭的系统中，一个与外界影响隔绝的系统，能量是守恒的，因此表现得像物质一样。在这样一个系统中，所有可能形式的能量的总和是恒定的，尽管任何一种能量的数量都可能发生变化。如果我们把整个宇宙看作一个封闭的系统，我们可以自豪地和十九世纪的物理学家一起宣布，宇宙的能量是不变的，它的任何部分都不可能被创造或毁灭。

Once this important work was done, further progress was rapid. It was soon recognized that these kinds o f energy, mechanical and heat, are only two o f its many forms. Everything which can be converted into either of them is also a form of energy. The radiation given off by the sun is energy, for part of it is transformed into heat on the earth. A n electric current possesses energy, for it heats a wire or turns the wheels of a motor. Coal represents chemical energy, liberated as heat when the coal burns. In every event in nature one form of energy is being converted into another, always at some well-defined rate o f exchange. In a closed system, one isolated from external influences, the energy is conserved and thus behaves like a substance. The sum o f all possible forms o f energy in such a system is constant, although the amount o f any one kind may be changing. I f we regard the whole universe as a closed system, we can proudly announce with the physicists of the nineteenth century that the energy o f the universe is invariant, that no part of it can ever be created or destroyed.

那么，我们的两个物质概念就是物质和能量。两者都遵循守恒定律：孤立系统的质量和总能量都不会改变。

O ur two concepts of substance are, then, matter and energy. Both obey conservation laws: A n isolated system cannot change either in mass or in total energy.

物质有重量，但能量没有重量。因此，我们有两个不同的概念和两条守恒定律。这些想法是否仍然值得认真对待？或者，这个看似有理有据的图景是否已经发生了改变？

Matter has weight but energy is weightless. We have therefore two different concepts and two conservation laws. Are these ideas still to be taken seriously? O r has this apparently well-founded picture been changed in

新的发展是否已经显现？答案是肯定的！这两个概念的进一步变化与相对论有关。我们稍后会回到这一点。

the light of newer developments? It has! Further changes in the two concepts are connected with the theory o f relativity. We shall return to this point later.

哲学背景

T H E P H I L O S O P H I C A L B A C K G R O U N D

科学研究的结果常常迫使哲学家改变对问题的认识，而这些问题远远超出了科学本身的有限领域。科学的目的是什么？对试图描述自然的理论的要求是什么？这些问题虽然超出了物理学的范围，但却与物理学密切相关，因为科学是这些问题产生的材料。哲学概括必须建立在科学成果的基础上。然而，一旦形成并被广泛接受，它们往往会通过指明许多可能的程序路线之一来影响科学思想的进一步发展。成功地反抗公认的观点会带来意想不到的、完全不同的发展，成为新哲学方面的源泉。

The results of scientific research very often force a change in the philosophical view of problems which extend far beyond the restricted domain of science itself. What is the aim of science? What is demanded of a theory which attempts to describe nature? These questions, although exceeding the bounds of physics, are intimately related to it, since science forms the material from which they arise. Philosophical generalizations must be founded on scientific results. Once formed and widely accepted, however, they very often influence the further development o f scientific thought by indicating one o f the many possible lines of procedure. Successful revolt against the accepted view results in unexpected and completely different developments, becoming a source of new philosophical aspects.

如果没有物理学史上的例子来说明，这些言论听起来必然是模糊和毫无意义的。

These remarks necessarily sound vague and pointless until illustrated by examples quoted from the history of physics.

我们在此试图描述关于科学目的的第一批哲学思想。这些思想极大地影响了物理学的发展，直到近一百年前，新证据、新事实和新理论的出现迫使人们抛弃这些思想，而这些新证据、新事实和新理论又为科学提供了新的背景。

We shall here try to describe the first philosophical ideas on the aim of science. These ideas greatly influenced the development o f physics until nearly a hundred years ago, when their discarding was forced by new evidence, new facts and theories, which in their turn formed a new background for science.

从希腊哲学到现代物理学，在整个科学史上，人们一直试图将自然现象的表面复杂性简化为一些简单的基本思想和关系。这是所有自然哲学的基本原理。它甚至在原子论者的著作中也有所体现。二十三个世纪前，德谟克利特写道：按照惯例，甜就是甜的，按照惯例，苦就是 苦的，按照惯例，热就是热的，按照惯例，冷就是冷的， 按照惯例，颜色就是颜色。但实际上存在 原子和虚空。也就是说，感官对象被认为 是真实的，人们习惯上也认为它们是真实的， 但事实上它们不是。只有原子和虚空是 真实的。

In the whole history of science from Greek philosophy to modern physics there have been constant attempts to reduce the apparent complexity of natural phenomena to some simple fundamental ideas and relations. This is the underlying principle of all natural philosophy. It is expressed even in the work of the Atomists. Twenty-three centuries ago Democritus wrote: By convention sweet is sweet, by convention bitter is bitter, by convention hot is hot, by convention cold is cold, by convention colour is colour. But in reality there are atoms and the void. That is, the objects of sense are supposed to be real and it is customary to regard them as such, but in truth they are not. Only the atoms and the void are real.

这种思想在古代哲学中只不过是一种奇妙的想象而已。

This idea remains in ancient philosophy nothing more than an ingenious figment o f the imagination.

希腊人并不知道与后续事件有关的自然法则。将理论与实验联系起来的科学实际上始于伽利略的工作。我们追寻着通往运动定律的最初线索。在两百年的科学研究中，力和物质是理解自然的所有努力的基础概念。我们无法想象其中之一没有另一个，因为物质通过对其他物质的作用来证明其作为力源的存在。

Laws of nature relating subsequent events were unknown to the Greeks. Science connecting theory and experiment really began with the work of Galileo. We have followed the initial clues leading to the laws of motion. Throughout two hundred years of scientific research force and matter were the underlying concepts in all endeavours to understand nature. It is impossible to imagine one without the other because matter demonstrates its existence as a source of force by its action on other matter.

让我们考虑最简单的例子：两个粒子之间有作用力。最容易想象的力是引力和斥力。在这两种情况下，力矢量都位于连接两个粒子的线上。

Let us consider the simplest example: two particles with forces acting between them. The easiest forces to imagine are those o f attraction and repulsion. In both cases the force vectors lie on a line connecting the

物质点。对简单性的要求导致了粒子相互吸引或排斥的画面；对作用力方向的任何其他假设都会给出更为复杂的画面。

material points. The demand for simplicity leads to the picture of particles attracting or repelling each other; any other assumption about the direction of the acting forces would give a much more complicated picture.

我们能否对力矢量的长度做出同样简单的假设？即使我们想避免太过特殊的假设，我们仍然可以说一件事：任何两个给定粒子之间的力只取决于它们之间的距离，就像引力一样。

Can we make an equally simple assumption about the length o f the force vectors? Even if we want to avoid too special assumptions we can still say one thing: the force between any two given particles depends only on the distance between them, like gravitational forces.

这似乎很简单。可以想象出更复杂的力，比如那些不仅取决于距离还取决于两个粒子速度的力。以物质和力作为我们的基本概念，我们很难想象出比力沿着连接粒子的线作用且仅取决于距离更简单的假设。

This seems simple enough. M uch more complicated forces could be imagined, such as those which might depend not only on the distance but also on the velocities of the two particles. With matter and force as our fundamental concepts, we can hardly imagine simpler assumptions than that forces act along the line connecting the particles and depend only on the distance.

但是，仅靠这种力就能描述所有物理现象吗？

But is it possible to describe all physical phenomena by forces of this kind alone?

力学在其所有分支学科中都取得了巨大成就，它在天文学发展中取得了显著成功，它的思想被应用于显然不同且非机械性质的问题，所有这些都促使人们相信，

The great achievements of mechanics in all its branches, its striking success in the development o f astronomy, the application of its ideas to problems apparently different and non-mechanical in character, all these things contributed to the belief that it is possible

用不变物体之间的简单力来描述所有自然现象。在伽利略时代之后的两个世纪里，这种有意识或无意识的努力几乎体现在所有的科学创造中。十九世纪中叶，亥姆霍兹明确阐述了这一点：因此，最后，我们发现物理材料科学的问题 是将自然现象归结为 不变的吸引力和排斥力，其强度完全取决于距离。这个问题的可解性是完全理解 自然的条件。

to describe all natural phenomena in terms o f simple forces between unalterable objects. Throughout the two centuries following Galileo’s time such an endeavour, conscious or unconscious, is apparent in nearly all scientific creation. This was clearly formulated by Helmholtz about the middle of the nineteenth century: Finally, therefore, we discover the problem of physical material science to be to refer natural phenomena back to unchangeable attractive and repulsive forces whose intensity depends wholly upon distance. The solubility of this problem is the condition of the complete comprehensibility of nature.

因此，根据亥姆霍兹的观点，科学的发展路线是确定的，并严格遵循固定的路线：

Thus, according to Helmholtz, the line of development o f science is determined and follows strictly a fixed course :

一旦 自然现象被简化为简单力，并且 证明这是现象唯一 能够被简化的方式，它的使命就将结束。

And its vocation will be ended as soon as the reduction of natural phenomena to simple forces is complete and the proof given that this is the only reduction of which the phenomena are capable.

这种观点在 20 世纪的物理学家看来既愚钝又幼稚。他一想到伟大的科学研究冒险这么快就结束了，一副平淡无奇却万无一失的宇宙图景就被确立，就会感到害怕。

This view appears dull and naive to a twentieth-century physicist. It would frighten him to think that the great adventure of research could be so soon finished, and an unexciting if infallible picture o f the universe established for all time.

虽然这些原则将所有事件的描述简化为简单的力，但它们确实没有回答力应该如何依赖于距离的问题。对于不同的现象，这种依赖关系可能不同。对不同事件引入多种不同类型的力的必要性是

Although these tenets would reduce the description of all events to simple forces, they do leave open the question o f just how the forces should depend on distance. It is possible that for different phenomena this dependence is different. The necessity of introducing many different kinds of force for different events is

从哲学角度来看，这当然不能令人满意。然而，这种由亥姆霍兹最清楚地阐述的所谓 机械观在当时发挥了重要作用。物质运动论的发展是受机械观直接影响的最伟大成就之一。

certainly unsatisfactory from a philosophical point of view. Nevertheless this so-called mechanical view, most clearly formulated by Helmholtz, played an important role in its time. The development of the kinetic theory of matter is one o f the greatest achievements directly influenced by the mechanical view.

在见证它的衰落之前，让我们暂时接受上个世纪物理学家的观点，看看我们能从他们对外部世界的描绘中得出什么结论。

Before witnessing its decline, let us provisionally accept the point of view held by the physicists of the past century and see what conclusions we can draw from their picture of the external world.

物质理论中的理论

T H E K IN E T IC T H E O R Y O F M A T T E R

能否用粒子通过简单的力相互作用的运动来解释热现象？一个封闭的容器中含有一定质量的气体（例如空气），温度一定。通过加热，我们可以提高温度，从而增加能量。但是这种热量与运动有什么关系呢？

Is it possible to explain the phenomena o f heat in terms of the motions o f particles interacting through simple forces? A closed vessel contains a certain mass of gas— air, for example— at a certain temperature. By heating we raise the temperature, and thus increase the energy. But how is this heat connected with motion?

这种联系的可能性既体现在我们暂时接受的哲学观点上，也体现在运动产生热量的方式上。如果每个问题都是机械问题，那么热量就一定是机械能。动能论的目的就是提出这样一种概念：

The possibility of such a connection is suggested both by our tentatively accepted philosophical point of view and by the way in which heat is generated by motion. Heat must be mechanical energy if every problem is a mechanical one. The object of the kinetic theory is to present the concept of just in this

方式。根据这一理论，气体是大量粒子或分子的集合，

way. According to this theory a gas is a congregation of an enormous number of particles, or m olecules,

向各个方向移动，相互碰撞，并且每次碰撞都会改变运动方向。

moving in all directions, colliding w ith each other and changing in direction o f motion with each collision.

分子间必定存在一个平均速度，正如在一个庞大的人类社会中，存在一个平均

There must exist an average speed of molecules, just as in a large human community there exists an average

6度

年龄或平均财富。因此，每个粒子将有一个平均动能。容器中的热量越多，平均动能就越大。因此，根据这种图景，热量并不是不同于机械能量的特殊能量形式，而只是分子运动的动能。任何确定的温度都对应着每个分子确定的平均动能。事实上，这并不是一个任意的假设。如果我们想形成一个一致的物质力学图景，我们就不得不把分子的动能视为气体温度的量度。

age, or an average wealth. There will therefore be an average kinetic energy per particle. More heat in the vessel means a greater average k in etic energy. Thus heat, according to th is picture, is not a special form o f energy different from the mechanical one but is just the kinetic energy o f molecular motion. T o any definite temperature there corresponds a definite average kinetic energy per molecule. This is, in fact, not an arbitrary assumption. We are forced to regard the kinetic energy o f a molecule as a measure o f the temperature o f the gas if we wish to form a consistent mechanical picture of matter.

这一理论不只是一种想象而已。

This theory is more than a play of the imagination.

可以看出，气体动力学理论不仅与实验相符，而且实际上可以更深刻地理解事实。这可以通过几个例子来说明。

It can be shown that the kinetic theory of gases is not only in agreement with experiment, but actually leads to a more profound understanding o f the facts. This may be illustrated by a few examples.

我们有一个由可自由移动的活塞封闭的容器。容器中装有一定量的气体，并保持恒定的温度。如果活塞最初处于某个位置的静止状态，则可以通过移除重量将其向上移动，通过增加重量将其向下移动。要将活塞向下推，必须使用力来抵抗气体的内部压力。根据动力学理论，这种内部压力的机制是什么？

We have a vessel closed by a piston which can move freely. The vessel contains a certain amount of gas to be kept at a constant temperature. I f the piston is initially at rest in some position, it can be moved upward by removing and downward by adding weight. To push the piston down force must be used acting against the inner pressure of the gas. What is the mechanism of this inner pressure according to the kinetic theory?

构成气体的大量粒子向四面八方移动。它们轰击壁和活塞，像球被扔到墙上一样反弹回来。大量粒子的持续轰击使活塞保持在一定高度，

A tremendous number of particles constituting the gas are moving in all directions. They bombard the walls and the piston, bouncing back like balls thrown against a wall. This continual bombardment by a great number o f particles keeps the piston at a certain height by

抵消作用在活塞和重物上的向下的重力。在一个方向上有恒定的重力，在另一个方向上有来自分子的非常多的不规则打击。如果要达到平衡，所有这些小的不规则力对活塞的净效应必须等于重力的净效应。

opposing the force of gravity acting downward on the piston and the weights. In one direction there is a constant gravitational force, in the other very many irregular blows from the molecules. The net effect on the piston of all these small irregular forces must be equal to that of the force of gravity if there is to be equilibrium.

假设活塞被压下，将气体压缩到原来体积的一小部分，比如说一半，而温度保持不变。根据动能论，我们能期待发生什么？轰击产生的力会比以前更有效还是更无效？粒子现在更紧密地堆积在一起。虽然平均动能仍然相同，但粒子与活塞的碰撞现在将更频繁地发生，因此总力将更大。从中可以清楚地看出

Suppose the piston were pushed down so as to compress the gas to a fraction of its former volume, say one-half, its temperature being kept unchanged. What, according to the kinetic theory, can we expect to happen? Will the force due to the bombardment be more or less effective than before? The particles are now packed more closely. Although the average kinetic energy is still the same, the collisions o f the particles with the piston will now occur more frequently and thus the total force will be greater. It is clear from this

动力学理论所呈现的图像表明，要使活塞保持在这个较低的位置，需要更大的重量。这个简单的实验事实众所周知，但从物质的动力学观点来看，它的预测是合乎逻辑的。

picture presented by the kinetic theory that to keep the piston in this lower position more weight is required. This simple experimental fact is well known, but its prediction follows logically from the kinetic view of matter.

考虑另一种实验装置。取两个容器，容器中装有相同体积的不同气体，例如氢气和氮气，两者的温度相同。假设两个容器用相同的活塞封闭，活塞上有相同的重量。简而言之，这意味着两种气体具有相同的体积、温度和压力。由于温度相同，根据理论，每个粒子的平均动能也相同。由于压力相等，两个活塞受到的总力相同。平均而言，每个粒子都携带相同的能量，两个容器的体积也相同。因此，尽管气体的化学性质不同，但每个容器中的分子数 必须相同 。这一结果对于理解许多化学现象非常重要。这意味着，在一定温度和压力下，给定体积中的分子数不是特定气体的特征，而是所有气体的特征。最令人惊讶的是，动能论不仅预测了这样一个通用数字的存在，而且使我们能够确定它。我们很快就会回到这一点。

Consider another experimental arrangement. Take two vessels containing equal volumes of different gases, say hydrogen and nitrogen, both at the same temperature. Assume the two vessels are closed with identical pistons, on which are equal weights. This means, briefly, that both gases have the same volume, temperature, and pressure. Since the temperatue is the same, so, according to the theory, is the average kinetic energy per particle. Since the pressures are equal, the two pistons are bombarded with the same total force. O n the average every particle carries the same energy and both vessels have the same volume. Therefore, the number o f molecules in each must be the same, although the gases are chemically different. This result is very im portant for the understanding o f many chemical phenomena. It means that the number o f molecules in a given volume, at a certain temperature and pressure, is something which is characteristic, not o f a particular gas, but of all gases. It is most astonishing that the kinetic theory not only predicts the existence o f such a universal number, but enables us to determine it. To this point we shall return very soon.

物质动能论定量和定性地解释了实验确定的气体定律。此外，该理论不受限制

The kinetic theory o f matter explains quantitatively as well as qualitatively the laws of gases as determined by experiment. Furthermore, the theory is not restricted

气体，尽管它最大的成功是在这一领域。

to gases, although its greatest successes have been in this domain.

气体可以通过降低温度而液化。物质温度的下降意味着其粒子平均动能的下降。

A gas can be liquefied by means of a decrease of temperature. A fall in the temperature of matter means a decrease in the average kinetic energy of its particles.

由此可见，液体粒子的平均动能小于相应气体粒子的平均动能。

It is therefore clear that the average kinetic energy o f a liquid particle is smaller than that o f a corresponding gas particle.

液体中粒子运动的惊人表现首次被称作布朗运动，这一非凡现象如果没有物质运动论，将仍然是一个神秘而不可理解的现象。植物学家布朗首次观察到了这一现象，并在 80 年后，即本世纪初对其进行了解释。观察布朗运动所需的唯一仪器是显微镜，甚至不需要特别好的显微镜。

A striking manifestation o f the motion o f particles in liquids was given for the first time by the so-called Brownian movement, a remarkable phenomenon which would remain quite mysterious and incomprehensible without the kinetic theory of matter. It was first observed by the botanist Brown, and was explained eighty years later, at the beginning of this century. The only apparatus necessary for observing Brownian motion is a microscope, which need not even be a particularly good one.

布朗正在研究某些植物的花粉粒，即：

Brown was working with grains of pollen of certain plants, that is:

尺寸异常大的颗粒或粒子，长度从 四千分之一英寸到约千分之五英寸不等 。

particles or granules of unusually large size varying from one four-thousandth to about five-thousandth of an inch in length.

他进一步报告说：

H e reports further:

当检查这些粒子浸入水中的形态时 ，我发现其中许多粒子显然在运动……

While examining the form of these particles immersed in water, I observed many of them evidently in motion. . . .

经过反复观察后，这些运动让我确信， 它们既不是由 流体中的电流引起的，也不是由流体的逐渐蒸发引起的，而是属于 粒子本身的。

These motions were such as to satisfy me, after frequently repeated observation, that they arose neither from current in the fluid nor from its gradual evaporation, but belonged to the particle itself.

布朗观察到的是，当颗粒悬浮在水中时，通过显微镜可以看到它们不停地搅动。这真是一个令人印象深刻的景象！

What Brown observed was the unceasing agitation o f the granules when suspended in water and visible through the microscope. It is an impressive sigh t!

选择特定植物是否对这一现象至关重要？布朗通过对许多不同的植物重复实验来回答这个问题，他发现，所有颗粒，如果足够小，在悬浮在水中时都会表现出这种运动。此外，他还发现无机和有机物质的极小颗粒中也存在同样的不安、不规则的运动。即使是狮身人面像的碎块，他也观察到了同样的现象！

Is the choice of particular plants essential for the phenomenon? Brown answered this question by repeating the experiment with many different plants, and found that all the granules, if sufficiently small, showed such motion when suspended in water. Furthermore, he found the same kind o f restless, irregular motion in very small particles of inorganic as well as organic substances. Even with a pulverized fragment of a sphinx he observed the same phenomenon !

如何解释这种运动？它似乎与所有以前的经验相矛盾。每三十秒检查一个悬浮粒子的位置，就会发现其路径的奇妙形状。令人惊奇的是运动似乎具有永恒性。如果没有外力推动，放置在水中的摆动钟摆很快就会静止。永不减弱的运动的存在似乎与所有经验相悖。物质运动理论出色地阐明了这一难题。

How is this motion to be explained? It seems contradictory to all previous experience. Examination of the position of one suspended particle, say every thirty seconds, reveals the fantastic form o f its path. The amazing thing is the apparently eternal character of the motion. A swinging pendulum placed in water soon comes to rest if not impelled by some external force. The existence of a never-diminishing motion seems contrary to all experience. This difficulty was splendidly clarified by the kinetic theory o f matter.

即使用我们最强大的显微镜观察水，我们也无法看到物质运动理论所描绘的分子及其运动。必须得出这样的结论：如果水是粒子集合的理论是正确的，那么粒子的大小一定超出了最佳显微镜的可见范围。尽管如此，我们还是坚持这一理论，并假设它代表了现实的一致图景。

Looking at water through even our most powerful microscopes we cannot see molecules and their motion as pictured by the kinetic theory of matter. It must be concluded that if the theory of water as a congregation of particles is correct, the size of the particles must be beyond the limit of visibility of the best microscopes. Let us nevertheless stick to the theory and assume that it represents a consistent picture of reality.

通过显微镜可见的布朗粒子受到构成水本身的较小粒子的轰击。如果被轰击的粒子足够小，布朗运动就会存在。它之所以存在，是因为这种轰击不是从各个方向均匀的，而且由于其不规则和随机性，无法平均化。因此，观察到的运动是不可观察运动的结果。大粒子的行为在某种程度上反映了分子的行为，可以说，放大倍数很高，以至于可以通过显微镜看到。布朗粒子路径的不规则和随机性反映了构成物质的较小粒子路径的类似不规则性。因此，我们可以理解，对布朗运动的定量研究可以让我们更深入地了解物质的动力学理论。显然，可见的布朗运动取决于不可见的轰击分子的大小。如果轰击分子不具有一定量的能量，或者换句话说，如果它们没有质量和速度，就根本不会有布朗运动。因此，研究布朗运动可以确定分子的质量也就不足为奇了。

The Brownian particles visible through a microscope are bombarded by the smaller ones composing the water itself. The Brownian movement exists if the bombarded particles are sufficiently small. It exists because this bombardment is not uniform from all sides and cannot be averaged out, owing to its irregular and haphazard character. The observed motion is thus the result of the unobservable one. The behaviour o f the big particles reflects in some way that o f the molecules, constituting, so to speak, a magnification so high that it becomes visible through the microscope. The irregular and haphazard character of the path of the Brownian particles reflects a similar irregularity in the path o f the smaller particles which constitute matter. We can understand, therefore, that a quantitative study of Brownian movement can give us deeper insight into the kinetic theory o f matter. It is apparent that the visible Brownian motion depends on the size of the invisible bombarding molecules. There would be no Brownian motion at all if the bombarding molecules did not possess a certain amount o f energy or, in other words, if they did not have mass and velocity. That the study of Brownian motion can lead to a determination of the mass of a molecule is therefore not astonishing.

通过理论和实验的艰苦研究，动力学理论的定量特征得以形成。布朗运动现象是导致定量数据的线索之一。同样的数据可以EE

Through laborious research, both theoretical and experimental, the quantitative features of the kinetic theory were formed. The clue originating in the phenomenon of Brownian movement was one of those which led to the quantitative data. The same data can E E

可以通过不同的方法、从完全不同的线索出发来获得。所有这些方法都支持同一观点，这一点非常重要，因为它证明了物质动能论的内在一致性。

be obtained in different ways, starting from quite different clues. The fact that all these methods support the same view is most important, for it demonstrates the internal consistency o f the kinetic theory o f matter.

这里仅提及通过实验和理论得出的众多定量结果中的一个。

O nly one o f the many quantitative results reached by experiment and theory will be mentioned here.

假设我们有一克最轻的元素氢，并问：这一克氢中有多少粒子？答案不仅能描述氢，还能描述所有其他气体，因为我们已经知道在什么条件下两种气体具有相同数量的粒子。

Suppose we have a gram o f the lightest of all elements, hydrogen, and ask: how many particles are there in this one gram? The answer will characterize not only hydrogen but also all other gases, for we already know under what conditions two gases have the same number o f particles.

该理论使我们能够通过对悬浮粒子的布朗运动进行某些测量来回答这个问题。答案是一个惊人的大数字：3 后面跟着 23 个数字！一克氢中的分子数为 303,000,000,000,000,000,000,000。

The theory enables us to answer this question from certain measurements o f the Brownian motion o f a suspended particle. The answer is an astonishingly great number: a three followed by twenty-three other digits ! The number of molecules in one gram o f hydrogen is 303,000,000,000,000,000,000,000.

想象一下，一克氢分子的尺寸增大到可以通过显微镜看到：假设其直径变为五千分之一英寸，就像布朗粒子那样。那么，为了将它们紧密地包装起来，我们必须使用一个每边长约为四分之一英里的盒子！

Imagine the molecules of a gram of hydrogen so increased in size that they are visible through a microscope: say that the diameter becomes one five-thousandth of an inch, such as that of a Brownian particle. Then, to pack them closely, we should have to use a box each side of which is about one-quarter of a mile long !

我们可以通过将 1 除以上面引用的数字来轻松计算出一个这样的氢分子的质量。

We can easily calculate the mass o f one such hydrogen molecule by dividing 1 by the number quoted above.

答案是一个非常小的数字：0.000 000 000 000 000 000 000 0033 克，代表一个氢分子的质量。

The answer is a fantastically small num ber: 0.000 000 000 000 000 000 000 0033 gram, representing the mass of one molecule of hydrogen.

图 1

PLATE I

布朗运动实验只是 众多独立实验的一部分，这些实验最终确定 了这个在物理学中发挥着重要作用的数字。

experiments on Brownian motion are only some o f the many independent experiments leading to the determination o f this number which plays such an important part in physics.

在物质运动论及其一切重要成就中，我们看到了一般 哲学纲领的实现：将所有现象的解释归结 为物质粒子之间的相互作用 。

In the kinetic theory o f matter and in all its important achievements we see the realization o f the general philosophical program m e: to reduce the explanation o f all phenomena to the interaction between particles o f matter.

我们总结一下：

W e S u m m ar ize:

在力学中，移动身体的未来路径可以

I n m echa n ics the f u t u r e p a th o f a m o vin g bod y ca n be

预测和其过去揭示的不同现状和

p r e d ic te d a n d its p a s t d isclo se d i f its p resen t co n d itio n a n d

对其施加的压力是众所周知的。因此，例如，

the fo r c e s a ctin g upon it are k n o w n . T h u s , f o r e x a m p le , the

未来的道路是可以预见的。 主动力

f u t u r e p a t h s o f a l l p la n e ts ca n be fo r e s e e n . T h e a ctive fo r c e s

牛顿引力与距离有关吗

are N e w t o n ’ s g r a v ita tio n a l f o r c e s dep en d in g on the d istan ce

古典力学的伟大成果表明

a lo n e. T h e g re a t results o f c la s s ic a l m echa n ics su g g est th a t

机械观点可以一致地应用于所有分支

the m e ch a n ica l v ie w can be co n sisten tly a p p lie d to a l l branches

物理学中，所有现象都可以用动作来解释

o f p h y s ic s , that a l l p hen om en a can be e x p la in e d by the a ction

代表吸引力或排斥力的力，取决于

o f fo r c e s representing either attra ction or r e p u lsio n , depen din g

仅取决于不可改变的粒子之间的距离和作用。

o n ly upon distan ce a n d a ctin g betw een u n cha n gea ble p a r tic les.

在物质的动能论中，我们看到了这种观点是如何

I n the k in e tic theory o f m atter w e see h o w th is v ie w , a r is in g

来自我的机械问题，拥抱热潮

f r o m m e ch a n ica l p r o b le m s , em braces the p hen om en a o f heat

以及它如何导致结构的成功

a n d h o w it lea d s to a su cce s sfu l p ictu re o f the structure o f

事情。

m a tter.

二．

I I .

衰落

T H E D E C L I N E

机械观

O F T H E M E C H A N I C A L V I E W

衰落

T H E D E C L I N E

机械观

OF T H E M E C H A N I C A L VIEW

两种电流体 — 磁流体 — 第一种严肃的

T h e tw o electric f l u i d s — T h e m a g n etic f l u i d s — T h e f ir s t seriou s

难度—— 光速—— 光是一种物质——

d ifficu lty— T h e velo city o f lig h t— L i g h t a s a substa nce— T h e

色彩之谜——什么是波？——色彩的波理论

rid d le o f colou r— W h a t is a w a v e ? — T h e w a ve theory o f

光— 纵向或横向光波？— 以太

lig h t— L o n g itu d in a l or transverse lig h t w a v e s ?— E t h e r a n d

机械观

the m e ch a n ica l v ie w

两电流

T H E T W O E L E C T R I C F L U ID S

以下几页包含一些 非常简单的实验的枯燥报告。报告之所以枯燥无味， 不仅是因为实验的描述与它们的实际表现相比毫无趣味， 还因为实验的意义 只有在理论使之显现出来时才会显现出来。我们的 目的是提供一个 理论在物理学中的作用的惊人例子。

T h e following pages contain a dull report o f some very simple experiments. T h e account will be boring not only because the description o f experiments is uninteresting in comparison with their actual performance, but also because the meaning o f the experiments does not become apparent until theory makes it so. O u r purpose is to furnish a striking example o f the role o f theory in physics.

一根金属棒支撑在玻璃底座上，金属棒的两端通过导线连接到验电器上。验电器是什么？验电器是一种简单的装置，主要由两片金箔组成，悬挂在一小段金属的末端。

A metal bar is supported on a glass base, and each end of the bar is connected by means of a wire to an electroscope. What is an electroscope? It is a simple apparatus consisting essentially of two leaves of gold foil hanging from the end of a short piece of metal.

它被封装在玻璃罐或烧瓶中，金属只与非金属物体（称为绝缘体）接触。除了验电器和金属棒外，我们还配备了硬橡胶棒和一块法兰绒。

This is enclosed in a glass ja r or flask and the metal is in contact only with non-metallic bodies, called insulators. In addition to the electroscope and metal bar we are equipped with a hard rubber rod and a piece of flannel.

实验如下：我们看 71

The experiment is performed as follows: we look 71

看看叶子是否紧密地挂在一起，因为这是它们的正常位置。如果碰巧它们没有挂在一起，用手指触摸金属杆就可以将它们粘在一起。采取这些初步步骤后，用法兰绒使劲摩擦橡胶杆，使之与金属接触。叶子立刻分开了！即使杆被移除，它们仍然分开。

to see whether the leaves hang close together, for this is their normal position. I f by chance they do not, a touch of the finger on the metal rod will bring them together. These preliminary steps being taken, the rubber rod is rubbed vigorously with the flannel and brought into contact with the metal. The leaves separate at o n ce! They remain apart even after the rod is removed.

2. 我们进行另一项实验，使用与之前相同的装置，再次从紧密悬挂的金箔开始。这一次，我们并没有让摩擦棒真正接触金属，而只是靠近金属。再次，金箔分开。但有一点不同！当将棒拿开而未接触金属时，金箔会立即落回其正常位置，而不是保持分开。

2. We perform another experiment, using the same apparatus as before, again starting with the gold leaves hanging close together. This time we do not bring the rubbed rod into actual contact with the metal, but only near it. Again the leaves separate. But there is a difference ! When the rod is taken away without having touched the metal, the leaves immediately fall back to their normal position instead of remaining separated.

3. 让我们稍微改变一下装置，进行第三个实验。假设金属棒由两部分组成，连接在一起。我们用

3. Let us change the apparatus slightly for a third experiment. Suppose that the metal bar consists of two pieces, joined together. We rub the rubber rod with

法兰绒，然后再次将其靠近金属。同样的现象发生了，叶子分开了。但现在让我们将金属棒分成两个独立的部分，然后拿走橡胶棒。我们注意到，在这种情况下，叶子仍然分开，而不是像第二个实验中那样落回正常位置。

flannel and again bring it near the metal. The same phenomenon occurs, the leaves separate. But now let us divide the metal rod into its two separate parts and then take away the rubber rod. We notice that in this case the leaves remain apart, instead o f falling back to their normal position as in the second experiment.

很难对这些简单而幼稚的实验表现出热情的兴趣。在中世纪，进行这些实验的人可能会受到谴责；在我们看来，这些实验既乏味又不合逻辑。在只读过一次描述后，很难不感到困惑地重复这些实验。一些理论概念使它们变得可以理解。我们可以说得更多：几乎不可能想象这样的实验是作为偶然的游戏进行的，而没有事先存在或多或少关于其含义的明确想法。

It is difficult to evince enthusiastic interest in these simple and naive experiments. In the Middle Ages their performer would probably have been condemned; to us they seem both dull and illogical. It would be very difficult to repeat them, after reading the account only once, without becoming confused. Some notion o f the theory makes them understandable. We could say more: it is hardly possible to imagine such experiments performed as accidental play, without the pre-existence of more or less definite ideas about their meaning.

我们现在要指出一个非常简单和朴素的理论的基本思想，该理论可以解释所描述的所有事实。

We shall now point out the underlying ideas of a very simple and naive theory which explains all the facts described.

存在两种 电流体，一种称为正极（+），另一种 称为负极 （-）。它们有点像已经解释过的物质，因为数量可以增加或减少，但任何孤立系统中的总量都会保持不变。

There exist two electric fluids, one called positive ( + ) and the other negative ( - ) . They are somewhat like substance in the sense already explained, in that the amount can be enlarged or diminished, but the total in any isolated system is preserved. There is, how-

然而，这种情况与热、物质或能量的情况有着本质的区别。我们有两种电物质。除非以某种方式加以概括，否则这里不可能使用前面的货币类比。如果正负电流体恰好相互抵消，则物体是电中性的。一个人一无所有，要么是因为他真的一无所有，要么是因为他保险柜里存的钱正好等于他的债务总额。我们可以将他的账本中的借方和贷方条目与两种电流体进行比较。

ever, an essential difference between this case and that o f heat, matter or energy. We have two electrical substances. It is impossible here to use the previous analogy of money unless it is somehow generalized. A body is electrically neutral if the positive and negative electric fluids exactly cancel each other. A man has nothing, either because he really has nothing, or because the amount of money put aside in his safe is exactly equal to the sum of his debts. We can compare the debit and credit entries in his ledger to the two kinds of electric fluids.

该理论的下一个假设是，两种同类型的电流体相互排斥，而两种异类型的电流体相互吸引。这可以用以下图形表示：

The next assumption of the theory is that two electric fluids o f the same kind repel each other, while two of the opposite kind attract. This can be represented graphically in the following way:

最后需要进行一个理论假设：物体有两种，一种是流体可以在其中自由流动的物体，称为导体，另一种是流体不能在其中自由流动的物体，称为 绝缘体。在这种情况下，这种划分总是正确的，不必太过认真。理想的导体或绝缘体是一种虚构，它可以

A final theoretical assumption is necessary: There are two kinds of bodies, those in which the fluids can move freely, called conductors, and those in which they cannot, called insulators. As is always true in such cases, this division is not to be taken too seriously. The ideal conductor or insulator is a fiction which can

永远无法实现。金属、地球、人体都是导体的例子，尽管它们的质量并不一样好。玻璃、橡胶、瓷器等都是绝缘体。

never be realized. Metals, the earth, the human body, are all examples o f conductors, although not equally good. Glass, rubber, china, and the like are insulators.

空气只是部分绝缘体，这一点任何看过上述实验的人都知道。将静电实验的不良结果归咎于空气湿度（这会增加其导电性）始终是一个好借口。

A ir is only partially an insulator, as everyone who has seen the described experiments knows. It is always a good excuse to ascribe the bad results o f electrostatic experiments to the humidity o f the air, which increases its conductivity.

这些理论假设足以解释上述三个实验。我们将按照与之前相同的顺序再次讨论它们，但要根据电流体理论。

These theoretical assumptions are sufficient to explain the three experiments described. We shall discuss them once more, in the same order as before, but in the light o f the theory of electric fluids.

1 .

橡胶棒与正常条件下的所有其他物体一样，都是电中性的。它含有等量的正极和负极两种流体。通过用法兰绒摩擦，我们将它们分开。这种说法纯粹是惯例，因为它是将理论创造的术语应用于摩擦过程的描述。之后棒中多余的电称为负电，这个名称当然只是惯例问题。如果实验是用用猫毛摩擦的玻璃棒进行的，我们应该将多余的电称为正电，以符合公认的惯例。为了继续实验，我们用橡胶接触金属导体，将电流体带到金属导体上。在这里，电流体自由移动，遍布整个金属，包括金箔。由于负极对负极的作用是排斥，两片叶子试图尽可能远离彼此，结果是

The rubber rod, like all other bodies under normal conditions, is electrically neutral. It contains the two fluids, positive and negative, in equal amounts. By rubbing with flannel we separate them. This statement is pure convention, for it is the application of the terminology created by the theory to the description of the process of rubbing. The kind of electricity that the rod has in excess afterwards is called negative, a name which is certainly only a matter of convention. I f the experiments had been performed with a glass rod rubbed with cat’s fur we should have had to call the excess positive, to conform with the accepted convention. T o proceed with the experiment, we bring electric fluid to the metal conductor by touching it with the rubber. Here it moves freely, spreading over the whole metal including the gold leaves. Since the action of negative on negative is repulsion, the two leaves try to get as far from each other as possible and the result is

观察到的分离。金属放在玻璃或其他绝缘体上，这样只要空气的导电性允许，流体就会留在导体上。

the observed separation. The metal rests on glass or some other insulator so that the fluid remains on the conductor, as long as the conductivity of the air permits.

现在我们明白了为什么在开始实验之前必须接触金属。在这种情况下，金属、人体和地球形成一个巨大的导体，电流体被稀释得如此稀薄，以至于验电器上几乎没有残留物。

We understand now why we have to touch the metal before beginning the experiment. In this case the metal, the human body, and the earth form one vast conductor, with the electric fluid so diluted that practically nothing remains on the electroscope.

2. 本实验的开始方式与上一个实验完全相同。但是现在橡胶不再接触金属，而是靠近金属。导体中的两种流体可以自由移动，它们被分开，一种流体被吸引，另一种流体被排斥。当橡胶棒移开时，它们会再次混合，因为相反类型的流体会相互吸引。

2. This experiment begins just in the same way as the previous one. But instead of being allowed to touch the metal the rubber is now only brought near it. The two fluids in the conductor, being free to move, are separated, one attracted and the other repelled. They mix again when the rubber rod is removed, as fluids of opposite kinds attract each other.

3. 现在我们将金属分成两部分，然后取出金属棒。在这种情况下，两种液体不能混合，因此金箔保留了过量的电流体，并保持分离。

3. Now we separate the metal into two parts and afterwards remove the rod. In this case the two fluids cannot mix, so that the gold leaves retain an excess o f one electric fluid and remain apart.

根据这个简单的理论，这里提到的所有事实似乎都是可以理解的。同样的理论能做更多的事情，使我们不仅能够理解这些事实，还能理解“静电”领域的许多其他事实。每个理论的目的都是引导我们找到新的事实，提出新的实验，并发现新的现象和新的定律。举个例子就可以说明这一点。想象一下第二个实验中的变化。

In the light of this simple theory all the facts mentioned here seem comprehensible. The same theory does more, enabling us to understand not only these, but many other facts in the realm of “ electrostatics” . The aim of every theory is to guide us to new facts, suggest new experiments, and lead to the discovery of new phenomena and new laws. A n example will make this clear. Imagine a change in the second experiment.

假设我将橡胶棒靠近金属，同时用手指触摸导体。

Suppose I keep the rubber rod near the metal and at the same time touch the conductor with my finger.

接下来会发生什么？理论答案：被排斥的人

What will happen now? Theory answers: the repelled

液体（—）现在可以通过我的身体流出，结果只剩下一种液体，那就是阳性液体。

fluid ( —) can now make its escape through my body, with the result that only one fluid remains, the positive.

只有靠近橡皮棒的验电器片会保持分开。实际实验证实了这一预测。

O nly the leaves of the electroscope near the rubber rod will remain apart. An actual experiment confirms this prediction.

从现代物理学的角度来看，我们讨论的理论无疑是幼稚和不充分的。然而，它是一个很好的例子，展示了每个物理理论的特征。

The theory with which we are dealing is certainly naïve and inadequate from the point of view o f modern physics. Nevertheless it is a good example showing the characteristic features of every physical theory.

科学中没有永恒的理论。理论预测的某些事实总是会被实验推翻。每个理论都有其逐渐发展和胜利的时期，之后可能会经历迅速衰落。这里已经讨论过的物质热理论的兴衰是许多可能的例子之一。其他更深刻、更重要的例子将在后面讨论。科学的几乎每一个伟大进步都源于旧理论的危机，通过努力寻找摆脱困难的方法。我们必须审视旧思想、旧

There are no eternal theories in science. It always happens that some of the facts predicted by a theory are disproved by experiment. Every theory has its period of gradual development and triumph, after which it may experience a rapid decline. The rise and fall of the substance theory of heat, already discussed here, is one of many possible examples. Others, more profound and important, will be discussed later. Nearly every great advance in science arises from a crisis in the old theory, through an endeavour to find a way out of the difficulties created. We must examine old ideas, old

理论，尽管它们属于过去，因为这是理解新理论的重要性及其有效性范围的唯一方法。

theories, although they belong to the past, for this is the only way to understand the importance o f the new ones and the extent o f their validity.

在我们书的前几页，我们把调查员的角色比作侦探的角色，侦探在收集到必要的事实后，通过纯粹的思考找到正确的解决方案。从本质上讲，这种比较必须被视为非常肤浅。无论是在生活中还是在侦探小说中，犯罪都是给定的。侦探必须寻找信件、指纹、子弹、枪支，但至少他知道发生了谋杀案。但科学家则不然。不难想象有人对电一无所知，因为古人即使对电一无所知，也过得很幸福。给这个人金属、金箔、瓶子、硬橡胶棒、法兰绒，简而言之，就是进行我们三个实验所需的所有材料。他可能是一个非常有文化的人，但他可能会把酒倒进瓶子里，用法兰绒擦衣服，从来没有想过做我们描述的事情。对于侦探来说，犯罪是给定的，问题就是：谁杀了知更鸟？科学家必须至少在一定程度上承担自己的罪责，并进行调查。此外，他的任务不是解释一个案例，而是解释所有已经发生或可能继续发生的现象。

In the first pages o f our book we compared the role o f an investigator to that of a detective who, after gathering the requisite facts, finds the right solution by pure thinking. In one essential this comparison must be regarded as highly superficial. Both in life and in detective novels the crime is given. The detective must look for letters, fingerprints, bullets, guns, but at least he knows that a murder has been committed. This is not so for a scientist. It should not be difficult to imagine someone who knows absolutely nothing about electricity, since all the ancients lived happily enough without any knowledge of it. Let this man be given metal, gold foil, bottles, hard-rubber rod, flannel, in short, all the material required for performing our three experiments. H e may be a very cultured person, but he will probably put wine into the bottles, use the flannel for cleaning, and never once entertain the idea of doing the things we have described. For the detective the crime is given, the problem formulated: who killed Cock Robin? The scientist must, at least in part, commit his own crime, as well as carry out the investigation. Moreover, his task is not to explain just one case, but all phenomena which have happened or may still happen.

在引入流体概念时，我们看到了那些试图用物质和简单的力来解释一切的机械思想的影响

In the introduction o f the concept o f fluids we see the influence o f those mechanical ideas which attempt to explain everything by substances and simple forces

力在它们之间起作用。要了解机械观点是否可以应用于电现象的描述，我们必须考虑以下问题。给定两个小球，它们都带有电荷，也就是说，它们都携带过量的电流体。我们知道球体会相互吸引或排斥。但力是否只取决于距离？如果是，那么如何取决于距离？最简单的猜测似乎是，这种力与引力一样取决于距离，如果距离增加三倍，引力就会减弱到原来的九分之一。库仑进行的实验表明，这一定律确实有效。牛顿发现引力定律一百年后，库仑发现了电力对距离的类似依赖性。牛顿定律和库仑定律的两个主要区别是：引力引力始终存在，而电力只有当物体带电荷时才存在。在引力的情况下只有吸引力，但电力可以吸引或排斥。

acting between them. T o see whether the mechanical point of view can be applied to the description of electrical phenomena, we must consider the following problem. Two small spheres are given, both with an electric charge, that is, both carrying an excess o f one electric fluid. We know that the spheres will either attract or repel each other. But does the force depend only on the distance, and if so, how? The simplest guess seems to be that this force depends on the distance in the same way as gravitational force, which diminishes, say, to one-ninth of its former strength if the distance is made three times as great. The experiments performed by Coulomb showed that this law is really valid. A hundred years after Newton discovered the law of gravitation, Coulomb found a similar dependence o f electrical force on distance. The two major differences between Newton’s law and Coulom b’s law are: gravitational attraction is always present, while electric forces exist only if the bodies possess electric charges. In the gravitational case there is only attraction, but electric forces may either attract or repel.

这里出现了我们在考虑热时考虑的同一个问题。电流体是无重量物质吗？换句话说，一块金属无论是中性还是带电，其重量都一样吗？我们的秤没有显示出任何差异。我们得出结论，电流体也是无重量物质家族的成员。

There arises here the same question which we considered in connection with heat. A te the electrical fluids weightless substances or not? In other words, is the weight of a piece o f metal the same whether neutral or charged? O ur scales show no difference. We conclude that the electric fluids are also members of the family of weightless substances.

电学理论的进一步发展需要引入两个新概念。我们再次

Further progress in the theory of electricity requires the introduction o f two new concepts. Again we shall

避免严格的定义，0

avoid rigorous definitions, 0

而是使用类比

using instead analogies with

我们已经熟悉的概念。我们记得，区分热量本身和温度对于理解热现象是多么重要。在这里，区分电势和电荷也同样重要。这两个概念之间的区别可以通过类比来明确：电势—温度

concepts already familiar. We remember how essential it was for an understanding o f the phenomena of heat to distinguish between heat itself and temperature. It is equally important here to distinguish between electric potential and electric charge. The difference between the two concepts is made clear by the analogy: Electric potential— Temperature

电荷—热量

Electric charge— Heat

两个导体，例如两个不同大小的球体，可能具有相同的电荷，即一种电流体的过量电荷相同，但两种情况下的电位会有所不同，较小球体的电位较高，较大球体的电位较低。电流体的密度较大，因此在小导体上受到的压缩更大。由于排斥力必须随着密度的增加而增加，所以较小球体中电荷逃逸的趋势会比较大球体中更大。电荷从导体中逃逸的趋势是其电位的直接量度。为了清楚地显示电荷和电位之间的区别，我们将制定几个句子来描述加热体的行为，以及与带电导体有关的相应句子。

Two conductors, for example two spheres of different size, may have the same electric charge, that is the same excess of one electric fluid, but the potential will be different in the two cases, being higher for the smaller and lower for the larger sphere. The electric fluid will have greater density and thus be more compressed on the small conductor. Since the repulsive forces must increase with the density, the tendency of the charge to escape will be greater in the case o f the smaller sphere than in that of the larger. This tendency of charge to escape from a conductor is a direct measure of its potential . In order to show clearly the difference between charge and potential we shall formulate a few sentences describing the behaviour o f heated bodies, and the corresponding sentences concerning charged conductors.

热

H e a t

电

E l e c t r i c i t y

两具尸体，最初不同

Two bodies, initially at dif

两根绝缘导体，

Two insulated conductors,

不同的温度，达到

ferent temperatures, reach

最初在不同的电气

initially at different electric

之后温度相同

the same temperature after

潜力，很快达到

potentials, very quickly reach

一些时间如果被带入

some time if brought into

同样的潜力，如果

the same potential if brought

接触。

contact.

接触。

into contact.

等量的热量

Equal quantities of heat

等量的电

Equal amounts of electric

产生不同的变化

produce different changes of

收费

charge

生产

produce

不同的

different

两个物体的温度

temperature in two bodies

电位变化

changes of electric potential

如果它们的热容量

if their heat capacities are

如果两个物体的电性不同。

in two bodies if their elecdifferent.

能力不同

trical capacities are different

接触式温度计

A thermometer in contact

接触式验电器

An electroscope in contact

用身体表示——

with a body indicates— by

用导体表示

with a conductor indicates

汞的长度

the length of its mercury

— 通过分离

— by the separation of the

柱——它自己的温度金叶——它自己的电解质，因此有温度电位，因此 有身体的温度。

column— its own temperagold leaves— its own electure and therefore the temtric potential and therefore perature of the body.

的电势

the electric potential of the

导体。

conductor.

但这种类比不应过分。下面举一个例子来说明两者的相同之处和不同之处。

But this analogy must not be pushed too far. A n example shows the differences as well as the similarities.

如果热物体与冷物体接触，热量会从较热的物体流向较冷的物体。另一方面，假设我们有两个绝缘导体，它们带有相等但相反的电荷，一个带正电，另一个带负电。两者的电位不同。按照惯例，我们认为负电荷对应的电位低于正电荷对应的电位。如果将这两个导体放在一起或用电线连接起来，那么根据电流体理论，它们将不带电荷，因此也没有电位差。我们必须想象在电位差均衡的短暂时间内，电荷从一个导体“流”到另一个导体。但如何流动呢？

I f a hot body is brought into contact with a cold one, the heat flows from the hotter to the colder. O n the other hand, suppose that we have two insulated conductors having equal but opposite charges, one positive and the other negative. The two are at different potentials. By convention we regard the potential corresponding to a negative charge as lower than that corresponding to a positive charge. I f the two conductors are brought together or connected by a wire, it follows from the theory o f electric fluids that they will show no charge and thus no difference o f electric potential at all. We must imagine a “ flow” of electric charge from one conductor to the other during the short time in which the potential difference is equalized. But how?

是正极流体流向负极体，还是负极流体流向正极体？

Does the positive fluid flow to the negative body, or the negative fluid to the positive body?

在本文中介绍的材料中，我们没有在两种选择之间做出决定的依据。我们可以假设两种可能性中的任一种，或者假设流动在两个方向上同时进行。这只是一个采用惯例的问题，选择没有任何意义，因为我们不知道通过实验来决定这个问题的方法。进一步的发展导致了更为深刻的电学理论，回答了这个问题，而当用简单而原始的电流体理论来表述时，这个问题毫无意义。在这里，我们将简单地采用以下表达方式。

In the material presented here we have no basis for deciding between these two alternatives. We can assume either of the two possibilities, or that the flow is simultaneous in both directions. It is only a matter o f adopting a convention, and no significance can be attached to the choice, for we know no method of deciding the question experimentally. Further development leading to a much more profound theory of electricity gave an answer to this problem, which is quite meaningless when formulated in terms of the simple and primitive theory o f electric fluids. Here we shall simply adopt the following mode o f expression.

电流从电位较高的导体流向电位较低的导体。对于我们的两个导体，电流从正极流向负极。这种表达只是惯例问题，目前相当随意。整个困难表明热和电之间的类比绝不是完整的。

The electric fluid flows from the conductor having the higher potential to that having the lower. In the case o f our two conductors, the electricity thus flows from positive to negative. This expression is only a matter of convention and is at this point quite arbitrary. The whole difficulty indicates that the analogy between heat and electricity is by no means complete.

我们已经看到了用机械观点来描述静电学基本事实的可能性。对于磁现象来说，同样也是可能的。

We have seen the possibility o f adapting the mechanical view to a description of the elementary facts of electrostatics. The same is possible in the case of magnetic phenomena.

热磁流体

T H E M A G N E T IC F L U ID S

我们将按照与以前相同的方式进行，从非常简单的事实开始，然后寻求它们的理论解释。

We shall proceed here in the same manner as before, starting with very simple facts and then seeking their theoretical explanation.

1. 我们有两块长条形磁铁，一块自由悬挂在中央，另一块握在手中。两块磁铁的两端靠在一起，这样可以感觉到它们之间有很强的吸引力。

1. We have two long bar magnets, one suspended freely at its centre, the other held in the hand. The ends o f the two magnets are brought together in such a way that a strong attraction is noticed between them.

总是可以做到这一点。如果没有吸引力，我们必须转动磁铁并尝试另一端。如果条状物被磁化，就会发生一些事情。磁铁的两端称为磁极。为了继续实验，我们将手中的磁铁的磁极沿着另一块磁铁移动。注意到吸引力减小，当磁极到达悬挂磁铁的中间时，根本没有任何力的迹象。如果将磁极沿同一方向移动得更远，就会观察到排斥力，在悬挂磁铁的第二个磁极处达到最大强度。

This can always be done. I f no attraction results, we must turn the magnet and try the other end. Something will happen if the bars are magnetized at all. The ends of the magnets are called their poles. To continue with the experiment we move the pole of the magnet held in the hand along the other magnet. A decrease in the attraction is noticed and when the pole reaches the middle of the suspended magnet there is no evidence o f any force at all. I f the pole is moved farther in the same direction a repulsion is observed, attaining its greatest strength at the second pole of the hanging magnet.

2. 上述实验表明了另一个。每个

2. The above experiment suggests another. Each

磁铁有两个极。我们不能隔离其中一个极吗？

magnet has two poles. Can we not isolate one of them?

这个想法很简单：只要把一块磁铁掰成两块相等的部分。我们已经看到，一块磁铁的极点和另一块磁铁的中间之间没有力。

The idea is very simple: just break a magnet into two equal parts. We have seen that there is no force between the pole o f one magnet and the middle o f the other.

但实际上，磁铁断裂的结果令人惊讶且出乎意料。如果我们重复第 1 项中描述的实验，只悬挂半块磁铁，结果与之前完全相同！之前没有磁力痕迹的地方现在有一根强磁极。

But the result o f actually breaking a magnet is surprising and unexpected. I f we repeat the experiment described under 1, with only half a magnet suspended, the results are exactly the same as before ! Where there was no trace o f magnetic force previously, there is now a strong pole.

这些事实该如何解释呢？我们可以尝试仿照电流体理论来建立磁学理论。事实表明，磁学理论与静电现象一样，存在吸引力和排斥力。想象两个球形导体具有相同的电荷，一个带正电荷，另一个带负电荷。

How are these facts to be explained? We can attempt to pattern a theory of magnetism after the theory of electric fluids. This is suggested by the fact that here, as in electrostatic phenomena, we have attraction and repulsion. Imagine two spherical conductors possessing equal charges, one positive and the other negative.

这里的“相等”表示绝对值相同；

Here “ equal” means having the same absolute value;

例如，+ 5 和 - 5 具有相同的绝对值。让我们假设这些球体通过绝缘体（例如玻璃棒）连接。这种布置可以用从带负电的导体指向带正电的导体的箭头来表示。我们将整个东西称为电偶极子。很明显，两个这样的偶极子的行为与实验 1 中的条形磁铁完全一样。如果我们将我们的发明视为真实磁铁的模型，

+ 5 and - 5, for example, have the same absolute value. Let us assume that these spheres are connected by means of an insulator such as a glass rod. Schematically this arrangement can be represented by an arrow directed from the negatively charged conductor to the positive one. We shall call the whole thing an electric dipole. It is clear that two such dipoles would behave exactly like the bar magnets in experiment 1. I f we think of our invention as a model for a real magnet,

假设磁流体存在，我们可以说，磁铁只不过是一个 磁偶极子，两端有两种不同类型的流体。这个简单的理论模仿了电的理论，足以解释第一个实验。一端有吸引力，另一端有排斥力，中间有相等和相反的力平衡。

we may say, assuming the existence of magnetic fluids, that a magnet is nothing but a magnet dipole, having at its ends two fluids of different kinds. This simple theory, imitating the theory of electricity, is adequate for an explanation of the first experiment. There would be attraction at one end, repulsion at the other, and a balancing of equal and opposite forces in the middle.

但是第二个实验呢？在电偶极子的情况下，通过折断玻璃棒，我们得到两个孤立的极点。与第二个实验的结果相反，磁偶极子的铁棒也应该如此。因此，这种矛盾迫使我们引入一种更微妙的理论。我们可以设想磁铁由非常小的基本磁偶极子组成，这些偶极子不能被分解成单独的极点，而不是我们之前的模型。磁铁整体上是有序的，因为所有基本偶极子的方向都相同。

But what of the second experiment? By breaking the glass rod in the case of the electric dipole we get two isolated poles. The same ought to hold good for the iron bar of the magnetic dipole, contrary to the results of the second experiment. Thus this contradiction forces us to introduce a somewhat more subtle theory. Instead o f our previous model we may imagine that the magnet consists of very small elementary magnetic dipoles which cannot be broken into separate poles. Order reigns in the magnet as a whole, for all the elementary dipoles are directed in the same way.

我们立即明白了为什么切割磁铁会导致两个新的极点出现在新的一端，以及为什么这个更精确的理论可以解释实验 1 的事实

We see immediately why cutting a magnet causes two new poles to appear on the new ends, and why this more refined theory explains the facts o f experiment 1

以及 2。

as well as 2.

对于许多事实，更简单的理论就能给出解释，而细化似乎没有必要。让我们举个例子：我们知道磁铁会吸引

For many facts, the simpler theory gives an explanation and the refinement seems unnecessary. Let us take an example: We know that a magnet attracts pieces of

铁。为什么？在一块普通的铁上，两种磁性流体混合在一起，所以没有产生净效应。

iron. W h y? I n a piece o f ordinary iron the two magnetic fluids are mixed, so that no net effect results.

将正极靠近，就像对流体发出“分裂指令”，吸引铁的负流体，排斥正流体。铁和磁铁之间的吸引力随之而来。如果移除磁铁，流体会或多或少地恢复到其原始状态，这取决于它们记住外力指令的程度。

Bringing a positive pole near acts as a “ command of division” to the fluids, attracting the negative fluid of the iron and repelling the positive. The attraction between iron and magnet follows. I f the magnet is removed, the fluids go back to more or less their original state, depending on the extent to which they remember the commanding voice o f the external force.

这个问题的定量方面无需多言。利用两根非常长的磁化棒，我们可以研究它们的磁极靠近时产生的吸引力（或排斥力）。如果棒足够长，棒另一端的影响可以忽略不计。

Little need be said about the quantitative side o f the problem. With two very long magnetized rods we could investigate the attraction (or repulsion) of their poles when brought near one another. The effect o f the other ends of the rods is negligible if the rods are long enough.

吸引力或排斥力如何取决于两极之间的距离？库仑实验给出的答案是，这种对距离的依赖与牛顿万有引力定律和库仑静电定律相同。

How does the attraction or repulsion depend on the distance between the poles? The answer given by Coulomb’s experiment is that this dependence on distance is the same as in Newton’s law o f gravitation and Coulom b’s law of electrostatics.

我们在这个理论中再次看到了普遍观点的应用：倾向于用只取决于距离、作用于不变粒子之间的吸引力和排斥力来描述所有现象。

We see again in this theory the application o f a general point of view: the tendency to describe all phenomena by means o f attractive and repulsive forces depending only on distance and acting between unchangeable particles.

应该提到一个众所周知的事实，因为稍后我们会用到它。地球是一个巨大的磁偶极子。没有丝毫的解释来说明为什么这是真的。北极大约是地球的负磁极（—），南极是地球的正磁极（+）。正和负的名称是

O ne well-known fact should be mentioned, for later we shall make use of it. The earth is a great magnetic dipole. There is not the slightest trace o f an explanation as to why this is true. The North Pole is approximately the minus ( —) and the South Pole the plus ( + ) magnetic pole of the earth. The names plus and minus are

这只是惯例问题，但一旦固定，就可以让我们在任何其他情况下指定磁极。垂直轴上支撑的磁针服从地球磁力的指挥。它将其 (+) 极指向北极，即地球的 (-) 磁极。

only a matter o f convention, but when once fixed, enable us to designate poles in any other case. A magnetic needle supported on a vertical axis obeys the command of the magnetic force of the earth. It directs its ( + ) pole toward the North Pole, that is, toward the ( —) magnetic pole of the earth.

虽然我们可以在本文介绍的电磁现象领域中始终如一地实行机械观点，但没有理由对此感到特别自豪或高兴。该理论的某些特征当然不令人满意，甚至令人沮丧。必须发明新种类的物质：两种电流体和基本磁偶极子。物质的丰富程度开始令人难以抗拒！

Although we can consistently carry out the mechanical view in the domain of electric and magnetic phenomena introduced here, there is no reason to be particularly proud or pleased about it. Some features of the theory are certainly unsatisfactory if not discouraging. New kinds of substances had to be invented: two electric fluids and the elementary magnetic dipoles. The wealth of substances begins to be overwhelming !

这些力很简单。它们可以用类似的方式表达引力、电力和磁力。但这种简单性的代价很高：引入了新的无重量物质。这些都是相当人为的概念，与基本物质质量毫无关系。

The forces are simple. They are expressible in a similar way for gravitational, electric, and magnetic forces. But the price paid for this simplicity is high: the introduction of new weightless substances. These are rather artificial concepts, and quite unrelated to the fundamental substance, mass.

首次交易困难

T H E F IR S T S E R IO U S D I F F I C U L T Y

现在我们来谈谈在运用我们的一般哲学观点时遇到的第一个重大困难。后面会指出，这一困难与另一个更严重的困难一起，彻底摧毁了“所有现象都可以用机械方法解释”这一信念。

We are now ready to note the first grave difficulty in the application of our general philosophical point of view. It will be shown later that this difficulty, together with another even more serious, caused a complete breakdown of the belief that all phenomena can be explained mechanically.

电学作为科学技术的一个分支学科的巨大发展始于

The tremendous development o f electricity as a branch o f science and technique began with the dis-

电流的起源。在科学史上，我们发现了极少数意外事件似乎发挥了重要作用的例子之一。青蛙腿抽搐的故事有很多不同的讲述方式。无论细节是否真实，毫无疑问，伽伐尼的意外发现促使伏打在十八世纪末制造出了所谓的伏打电池。这不再有任何实际用途，但它仍然为学校演示和教科书描述提供了一个非常简单的电流源示例。

covery of the electric current. Here we find in the history of science one of the very few instances in which accident seemed to play an essential role. The story of the convulsion of a frog’s leg is told in many different ways. Regardless of the truth concerning details, there is no doubt that Galvani’s accidental discovery led V olta at the end of the eighteenth century to the construction of what is known as a voltaic battery. This is no longer of any practical use, but it still furnishes a very simple example of a source of current in school demonstrations and in textbook descriptions.

其构造原理很简单。有几个玻璃杯，每个杯中都装有水和少量硫酸。每个玻璃杯中都有两块金属板，一块是铜板，另一块是锌板，浸入溶液中。

The principle of its construction is simple. There are several glass tumblers, each containing water with a little sulphuric acid. In each glass two metal plates, one copper and the other zinc, are immersed in the solution.

一块玻璃的铜板与下一块玻璃的锌板相连，因此只有第一块玻璃的锌板和最后一块玻璃的铜板保持未连接状态。我们可以通过相当灵敏的验电器检测出第一块玻璃中的铜和最后一块玻璃中的锌之间的电位差，如果

The copper plate of one glass is connected to the zinc of the next, so that only the zinc plate of the first and the copper plate of the last glass remain unconnected. We can detect a difference in electric potential between the copper in the first glass and the zinc in the last by means of a fairly sensitive electroscope if the number o f the

“元件”，即构成电池的带有板的玻璃，足够大。

“ elements” , that is, glasses with plates, constituting the battery, is sufficiently large.

我们引入了由几个元素组成的电池，只是为了获得可以用已经描述的设备轻松测量的东西。

It was only for the purpose of obtaining something easily measurable with apparatus already described that we introduced a battery consisting of several elements.

为了进一步讨论，单一元素也同样适用。铜的电位结果高于锌的电位。“较高”在这里是指 + 2 大于 - 2 。如果一个

For further discussion, a single element will serve just as well. The potential of the copper turns out to be higher than that of the zinc. “ H igher” is used here in the sense in which + 2 is greater than - 2 . I f one

如果将一个导体连接到自由铜板，将另一个导体连接到锌板，则两个导体都会带电，第一个带正电，另一个带负电。到目前为止，还没有出现特别新颖或引人注目的东西，我们可以尝试应用我们以前关于电位差的想法。我们已经看到，通过用导线连接两个导体，可以快速消除它们之间的电位差，这样电流就会从一个导体流向另一个导体。这个过程类似于通过热流使温度均衡。但这在伏打电池中有效吗？伏打在他的报告中写道，这些板的行为就像导体：

conductor is connected to the free copper plate and another to the zinc, both will become charged, the first positively and the other negatively. U p to this point nothing particularly new or striking has appeared, and we may try to apply our previous ideas about potential differences. We have seen that a potential difference between two conductors can be quickly nullified by connecting them with a wire, so that there is a flow o f electric fluid from one conductor to the other. This process was similar to the equalization o f temperatures by heat flow. But does this work in the case of a voltaic battery? Volta wrote in his report that the plates behave like conductors :

...带微弱电荷，其不断地作用，或者每次放电后电荷都会重新建立；总之，这提供了无限的电荷或对电流体施加了永久的作用或脉冲。

. . .feebly charged, which act unceasingly or so that their charge after each discharge re-establishes itself; which, in a word, provides an unlimited charge or imposes a perpetual action or impulsion of the electric fluid.

他的实验得出了惊人的结果，即铜板和锌板之间的电位差不会像两根带电导体通过导线连接时那样消失。电位差仍然存在，根据流体理论，它必然导致电流体从电位较高的水平（铜板）向电位较低的水平（锌板）持续流动。为了挽救流体理论，我们可以假设某种恒定的力会重新产生电位差并导致电流体流动。但从能量的角度来看，整个现象是惊人的。

The astonishing result of his experiment is that the potential difference between the copper and zinc plates does not vanish as in the case of two charged conductors connected by a wire. The difference persists, and according to the fluids theory it must cause a constant flow of electric fluid from the higher potential level (copper plate) to the lower (zinc plate). In an attempt to save the fluid theory, we may assume that some constant force acts to regenerate the potential difference and cause a flow o f electric fluid. But the whole phenomenon is astonishing from the standpoint of energy.

载流导线中会产生大量热量，如果

A noticeable quantity of heat is generated in the wire carrying the current, even enough to melt the wire if

它很细。因此，在电线中会产生热能。但整个伏打电池形成一个孤立系统，因为没有外部能量供应。如果我们想遵守能量守恒定律，我们必须找到转化发生的地方，以及产生热量的代价。不难发现电池中发生了复杂的化学过程，浸没的铜和锌以及液体本身都参与其中。从能量的角度来看，这是正在发生的转化链：化学能->流动电流体的能量，即电流->热量。伏打电池不会永远存在；电流流动引起的化学变化会使电池在一段时间后失效。

it is a thin one. Therefore, heat-energy is created in the wire. But the whole voltaic battery forms an isolated system, since no external energy is being supplied. I f we want to save the law of conservation o f energy we must find where the transformations take place, and at what expense the heat is created. It is not difficult to realize that complicated chemical processes are taking place in the battery, processes in which the immersed copper and zinc, as well as the liquid itself, take active parts. From the standpoint o f energy this is the chain o f transformations which are taking place: chemical energy-> energy of the flowing electric fluid, i.e., the current->heat. A voltaic battery does not last for ever; the chemical changes associated with the flow of electricity make the battery useless after a time.

这项实验实际上揭示了应用机械思想的巨大困难，对于第一次听说它的人来说，这听起来一定很奇怪。这项实验是由奥斯特在大约一百二十年前进行的。他报告说：

The experiment which actually revealed the great difficulties in applying the mechanical ideas must sound strange to anyone hearing about it for the first time. It was performed by Oersted about a hundred and twenty years ago. H e reports:

通过这些实验，似乎可以表明磁针是在电流装置的帮助下从其位置移动的，并且只有在电流电路闭合时才会移动，但在电流电路打开时则不会移动，正如几年前某些非常著名的物理学家徒劳地尝试过的那样。

By these experiments it seems to be shown that the magnetic needle was moved from its position by help of a galvanic apparatus, and that, when the galvanic circuit was closed, but not when open, as certain very celebrated physicists in vain attempted several years ago.

假设我们有一个伏打电池和一根导线。如果导线连接到铜板但不连接到锌板，则存在电位差，但没有电流可以流动。让我们假设导线弯曲成一个圆圈，圆圈中心有一个磁性

Suppose we have a voltaic battery and a conducting wire. I f the wire is connected to the copper plate but not to the zinc, there will exist a potential difference but no current can flow. Let us assume that the wire is bent to form a circle, in the centre of which a magnetic

放置针头，导线和针头位于同一平面。只要导线不接触锌板，就不会发生任何事情。没有力作用，现有的电位差对针头的位置没有任何影响。似乎很难理解为什么奥斯特所说的“非常著名的物理学家”会期待这样的影响。

needle is placed, both wire and needle lying in the same plane. Nothing happens so long as the wire does not touch the zinc plate. There are no forces acting, the existing potential difference having no influence whatever on the position of the needle. It seems difficult to understand why the “ very celebrated physicists” , as Oersted called them, expected such an influence.

但现在让我们把导线连接到锌板上。马上就会发生一件奇怪的事情。磁针从原来的位置转动。如果这本书的页面代表圆的平面，那么它的一个极点现在指向读者。效果是垂直于平面的力作用在磁极上。

But now let us join the wire to the zinc plate. Im mediately a strange thing happens. The magnetic needle turns from its previous position. One of its poles now points to the reader if the page of this book represents the plane of the circle. The effect is that o f a force, perpendicular to the plane, acting on the magnetic pole.

面对实验事实，我们很难避免对力的作用方向得出这样的结论。

Faced with the facts of the experiment, we can hardly avoid drawing such a conclusion about the direction of the force acting.

这个实验很有趣，首先，

This experiment is interesting, in the first place, be-

因为它展示了两个明显不同的现象——磁和电流之间的关系。

cause it shows a relation between two apparently quite different phenomena, magnetism and electric current.

还有更重要的方面。磁极和电流流过的导线小部分之间的力不能位于连接导线和针头的线上，也不能位于流动电流体的粒子和基本磁偶极子线上。力垂直于这些线！第一次出现了一种与我们根据机械观点打算将外部世界的所有作用归结为的力完全不同的力。我们记得，引力、静电力和磁力遵循牛顿和库仑定律，作用于两个吸引或排斥物体的连线上。

There is another aspect even more important. The force between the magnetic pole and the small portions of the wire through which the current flows cannot lie along lines connecting the wire and needle, or the particles o f flowing electric fluid and the elementary magnetic dipoles. The force is perpendicular to these lines! For the first time there appears a force quite different from that to which, according to our mechanical point of view, we intended to reduce all actions in the external world. We remember that the forces of gravitation, electrostatics, and magnetism, obeying the laws of Newton and Coulomb, act along the line adjoining the two attracting or repelling bodies.

罗兰在近六十年前进行的一项实验更加突出了这一困难。撇开技术细节不谈，这项实验可以描述如下。想象一个带电小球。进一步想象，这个球在一个圆圈内以磁针为中心快速移动。从原则上讲，这与奥斯特的实验相同，唯一的区别在于，我们采用的是电荷的机械运动，而不是普通电流。罗兰发现，结果确实类似于电流在圆形导线中流动时观察到的结果。磁铁受到垂直力的作用而偏转。

This difficulty was stressed even more by an experiment performed with great skill by Rowland nearly sixty years ago. Leaving out technical details, this experiment could be described as follows. Imagine a small charged sphere. Imagine further that this sphere moves very fast in a circle at the centre o f which is a magnetic needle. This is, in principle, the same experiment as Oersted’s, the only difference being that instead o f an ordinary current we have a mechanically effected motion of the electric charge. Rowland found that the result is indeed similar to that observed when a current flows in a circular wire. The magnet is deflected by a perpendicular force.

现在让我们让电荷移动得更快。作用在磁极上的力因此而增大；

Let us now move the charge faster. The force acting on the magnetic pole is, as a result, increased; the

与初始位置的偏转变得更加明显。

deflection from its initial position becomes more distinct.

这一观察结果带来了另一个严重的复杂情况。

This observation presents another grave complication.

力不仅不位于连接电荷和磁铁的线上，而且力的强度取决于电荷的速度。整个机械观点都基于这样的信念：所有现象都可以用仅取决于距离而不是速度的力来解释。

Not only does the force fail to lie on the line connecting charge and magnet, but the intensity o f the force depends on the velocity of the charge. The whole mechanical point o f view was based on the belief that all phenomena can be explained in terms o f forces depending only on the distance and not on the velocity.

罗兰德的实验结果无疑动摇了这种信念，但我们可以选择保守一点，在旧观念的框架内寻找解决办法。

The result o f Row land’s experiment certainly shakes this belief. Yet we may choose to be conservative and seek a solution within the frame o f old ideas.

这种困难，即在理论成功发展过程中突然出现的意外障碍，在科学中经常出现。有时，对旧观念进行简单的概括似乎至少暂时是一种很好的出路。例如，在目前的情况下，拓宽以前的观点并在基本粒子之间引入更普遍的力似乎就足够了。然而，很多时候，修补旧理论是不可能的，困难导致其无法继续发展。

Difficulties o f this kind, sudden and unexpected obstacles in the triumphant development o f a theory, arise frequently in science. Sometimes a simple generalization o f the old ideas seems, at least temporarily, to be a good way out. It would seem sufficient in the present case, for example, to broaden the previous point of view and introduce more general forces between the elementary particles. Very often, however, it is impossible to patch up an old theory, and the difficulties result in its

一个理论的没落和另一个理论的兴起。在这里，不仅仅是一根微小磁针的行为打破了看似有理有据、成功的机械理论。另一次攻击甚至更加猛烈，来自一个完全不同的角度。但这是另一个故事，我们以后再讲。

downfall and the rise o f a new one. Here it was not only the behaviour o f a tiny magnetic needle which broke the apparently well-founded and successful mechanical theories. Another attack, even more vigorous, came from an entirely different angle. But this is another story, and we shall tell it later.

速度

T H E V E L O C I T Y O F L IG H T

在伽利略的《 两门新科学》中，我们听到了大师和他的学生关于光速的对话：

In Galileo’s Two New Sciences we listen to a conversation of the master and his pupils about the velocity of light:

S agredo： 但是我们必须考虑光速是什么样的，有多大？它是瞬时的还是瞬间的，还是像其他运动一样需要时间？我们不能通过实验来确定吗？

S a g r e d o : But of what kind and how great must we consider this speed of light to be? Is it instantaneous or momentary or does it, like other motion, require time? Can we not decide this by experiment?

简单来说： 日常经验表明，光的传播是瞬间的；因为当我们看到远处发射的火炮时，闪光会毫不费力地到达我们的眼睛；但声音要经过一段明显的间隔才能传到耳朵。

Sim p licio : Everyday experience shows that the propagation of light is instantaneous; for when we see a piece of artillery fired, at great distance, the flash reaches our eyes without lapse of time; but the sound reaches the ear only after a noticeable interval.

S agredo： 好吧，辛普利西奥，从这个熟悉的经验中我唯一能推断出的就是，声音到达我们的耳朵时，传播的速度比光慢；它并没有告诉我光的到来是否是瞬间的，或者尽管速度极快，但仍需要时间。……

S a g r e d o : Well, Simplicio, the only thing I am able to infer from this familiar bit of experience is that sound, in reaching our ears, travels more slowly than light; it does not inform me whether the coming of the light is instantaneous or whether, although extremely rapid, it still occupies time. . . .

Salvia ti： 这些和其他类似观察的微小结论性曾促使我设计出一种方法，通过该方法可以准确地确定照明（即光的传播）是否真的是瞬时的......

S a l v ia t i: The small conclusiveness of these and other similar observations once led me to devise a method by which one might accurately ascertain whether illumination, i.e., propagation of light, is really instantaneous.. . .

萨尔维亚蒂继续解释他的实验方法。为了理解他的想法，让我们想象一下光速不仅是有限的，而且

Salviati goes on to explain the method o f his experiment. In order to understand his idea let us imagine that the velocity of light is not only finite, but also

光的运动速度变慢，就像慢动作电影一样。两个人， A 和 B，都戴着有盖的灯笼，彼此相距一英里。第一个人， A打开了他的灯笼。两人约定， B看到A 的灯后，也会打开他的灯笼。让我们假设在我们的

small, that the motion of light is slowed down, like that in a slow-motion film. Two men, A and B , have covered lanterns and stand, say, at a distance o f one mile from each other. The first man, A , opens his lantern. The two have made an agreement that B will open his the moment he sees A's light. Let us assume that in our

“慢动作”光在一秒钟内传播一英里。

“ slow motion” the light travels one mile in a second.

A 打开灯笼发出信号。B 一秒钟后看到信号并发出应答信号。A 在发出自己的信号两秒钟后收到了应答信号。

A sends a signal by uncovering his lantern. B sees it after one second and sends an answering signal. This is received by A two seconds after he had sent his own.

也就是说，如果光以每秒一英里的速度传播，那么假设 B 距离 A一英里，那么从 A 发出信号到B收到信号之间会间隔两秒。相反，如果A 不知道光速，但假设他的同伴遵守了协议，并且在B 打开灯笼两秒后他注意到 B 也打开了灯笼，那么他可以得出光速为每秒一英里的结论。

That is to say, if light travels with a speed o f one mile per second, then two seconds will elapse between A ’s sending and receiving a signal, assuming that B is a mile away. Conversely, if A does not know the velocity o f light but assumes that his companion kept the agreement, and he notices the opening o f B ’s lantern two seconds after he opened his, he can conclude that the speed of light is one mile per second.

以当时的实验技术，伽利略几乎不可能用这种方法测定光速。如果距离是一英里，他就必须探测到十万分之一秒的时间间隔！

With the experimental technique available at that time Galileo had little chance o f determining the velocity o f light in this way. I f the distance were a mile, he would have had to detect time intervals o f the order o f one hundred-thousandth of a second !

伽利略提出了确定光速的问题，但并没有解决这个问题。问题的提出往往比问题的解决更为重要，而解决这些问题可能只是数学或实验技巧的问题。提出新问题、新可能性，从新角度看待旧问题，需要创造性的想象力，这标志着科学的真正进步。

Galileo formulated the problem o f determining the velocity of light, but did not solve it. The formulation o f a problem is often more essential than its solution, which may be merely a matter o f mathematical or experimental skill. To raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks real advance in science.

惯性原理、能量守恒定律都是通过对已经众所周知的实验和现象进行新的、独到的思考而获得的。

The principle of inertia, the law o f conservation of energy were gained only by new and original thoughts about already well-known experiments and phenomena.

本书的后续内容中会有很多此类例子，其中会强调以新的眼光看待已知事实的重要性并描述新的理论。

M any instances o f this kind will be found in the following pages o f this book, where the importance o f seeing known facts in a new light will be stressed and new theories described.

回到确定光速这个相对简单的问题，我们可以说，令人惊讶的是，伽利略没有意识到他的实验可以由一个人更简单、更准确地完成。他可以在那里安装一面镜子，而不是让他的同伴站在远处，镜子会在收到信号后立即自动发回。

Returning to the comparatively simple question o f determining the velocity o f light, we may remark that it is surprising that Galileo did not realize that his experiment could be performed much more simply and accurately by one man. Instead o f stationing his companion at a distance he could have mounted there a mirror, which would automatically send back the signal immediately after receiving it.

大约 250 年后，斐索利用这一原理首次通过地面实验测定了光速。罗默更早之前就通过天文观测测定了光速，但精度较低。

About two hundred and fifty years later this very principle was used by Fizeau, who was the first to determine the velocity o f light by terrestrial experiments. It had been determined by Roemer much earlier, though less accurately, by astronomical observation.

显然，由于光速非常巨大，只有通过测量相当于地球和太阳系另一颗行星之间的距离，或者通过更先进的实验技术，才能测量光速。第一种方法是罗默的方法，第二种方法是斐索的方法。

It is quite clear that in view o f its enormous m agnitude, the velocity of light could be measured only by taking distances comparable to that between the earth and another planet of the solar system or by a great refinement o f experimental technique. The first method was that of Roemer, the second that o f Fizeau.

自从进行这些首次实验以来，这个代表光速的非常重要的数字已经被确定了很多次，而且准确度越来越高。

Since the days of these first experiments the very im portant number representing the velocity of light has been determined many times, with increasing accuracy.

在我们这个世纪，一种高度精炼的技术

In our own century a highly refined technique was

为此目的，迈克尔逊发明了一种真空管。这些实验的结果可以简单地表达为：真空中的光速约为每秒 186,000 英里，或每秒 300,000 公里。

devised for this purpose by Michelson. The result of these experiments can be expressed simply: The velocity o f light in vacuo is approximately 186,000 miles per second, or 300,000 kilometres per second.

光物质

L I G H T A S S U B S T A N C E

我们再次从几个实验事实开始。刚刚引用的数字与真空中的光速有关。

Again we start with a few experimental facts. The number just quoted concerns the velocity o f light in vacuo.

不受干扰时，光以这种速度穿过真空。如果我们抽出玻璃容器中的空气，我们就能透过它看东西。我们能看到行星、恒星、星云，尽管光从它们穿过真空到达我们的眼睛。我们可以透过容器看到里面是否有空气，这一简单事实表明空气的存在并不重要。因此，我们可以在普通房间内进行光学实验，其效果与没有空气时相同。

Undisturbed, light travels with this speed through empty space. We can see through an empty glass vessel if we extract the air from it. We see planets, stars, nebulae, although the light travels from them to our eyes through empty space. The simple fact that we can see through a vessel whether or not there is air inside shows us that the presence o f air matters very little. For this reason we can perform optical experiments in an ordinary room with the same effect as if there were no air.

最简单的光学事实之一是光的传播是直线的。我们将描述一个原始而幼稚的实验来证明这一点。在点光源前放置一个带孔的屏幕。点光源是一种非常小的光源，比如说，一盏关着的灯笼上的一个小开口。在远处的墙上，屏幕上的孔将呈现为暗色背景上的光。下图显示了这种现象与光的直线传播之间的联系。

O ne of the simplest optical facts is that the propagation of light is rectilinear. We shall describe a primitive and naive experiment showing this. In front of a point source is placed a screen with a hole in it. A point source is a very small source o f light, say, a small opening in a closed lantern. O n a distant wall the hole in the screen will be represented as light on a dark background. The next drawing shows how this phenomenon is connected with the rectilinear propagation of light.

所有这些现象，甚至更复杂的光、影、半影的情况，都可以EE

A ll such phenomena, even the more complicated cases in which light, shadow, and half-shadows appear, can E E

可以通过光在真空 或空气中沿直线传播的假设来解释。

be explained by the assumption that light, in vacuo or in air, travels along straight lines.

让我们再举一个例子，光穿过物质的情况。一束光穿过真空，落在玻璃板上。会发生什么？如果直线运动定律仍然有效，路径将是虚线所示的路径。

Let us take another example, a case in which light passes through matter. We have a light beam travelling through a vacuum and falling on a glass plate. What happens? I f the law of rectilinear motion were still valid, the path would be that shown by the dotted line.

但实际上并非如此。路径中有一个中断，如图所示。我们在这里观察到的是被称为 折射的现象。熟悉的现象

But actually it is not. There is a break in the path, such as is shown in the drawing. What we observe here is the phenomenon known as refraction. The familiar appear-

如果将一根棍子半浸在水中，它看起来似乎在中间弯曲，这是折射的众多表现形式之一。

ance o f a stick which seems to be bent in the middle if half-immersed in water is one of the many manifestations of refraction.

这些事实足以说明如何设计出一个简单的光机械理论。我们的目的是展示物质、粒子和力的概念如何渗透到光学领域，以及旧的哲学观点最终如何瓦解。

These facts are sufficient to indicate how a simple mechanical theory of light could be devised. O ur aim here is to show how the ideas of substances, particles, and forces penetrated the field of optics, and how finally the old philosophical point of view broke down.

这里的理论以其最简单、最原始的形式展现出来。我们假设所有发光物体都会发射光粒子或微粒，这些粒子落在我们的眼睛上，产生光的感觉。我们已经习惯于在机械解释需要时引入新物质，因此我们可以毫不犹豫地再次这样做。这些微粒必须以已知的速度沿直线穿过空旷的空间，将发光物体的信息带到我们的眼睛。所有表现出光直线传播的现象都支持微粒理论，因为这种运动正是为微粒规定的。该理论还非常简单地解释了镜子对光的反射，就像在弹性球撞墙的机械实验中所示的反射一样，如下图所示。

The theory here suggests itself in its simplest and most primitive form. Let us assume that all lighted bodies emit particles of light, or corpuscles, which, falling on our eyes, create the sensation of light. We are already so accustomed to introduce new substances, if necessary for a mechanical explanation, that we can do it once more without any great hesitation. These corpuscles must travel along straight lines through empty space with a known speed, bringing to our eyes messages from the bodies emitting light. A ll phenomena exhibiting the rectilinear propagation o f light support the corpuscular theory, for just this kind o f motion was prescribed for the corpuscles. The theory also explains very simply the reflection o f light by mirrors as the same kind of reflection as that shown in the mechanical experiment of elastic balls thrown against a wall, as the next drawing indicates.

折射的解释稍微困难一些。

The explanation of refraction is a little more difficult.

无需赘述，我们可以看出机械解释的可能性。例如，如果粒子落在玻璃表面，物质粒子可能会对它们施加力，这种力

Without going into details, we can see the possibility o f a mechanical explanation. I f corpuscles fall on the surface of glass, for example, it may be that a force is exerted on them by the particles o f the matter, a force

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奇怪的是，它只在物质的附近起作用。我们已经知道，作用在运动粒子上的任何力都会改变速度。如果光粒子上的净力是垂直于玻璃表面的吸引力，那么新的运动将位于原始路径线和垂直线之间。这个简单的解释似乎预示着光粒子理论的成功。然而，要确定该理论的实用性和有效性范围，我们必须研究新的、更复杂的事实。

which strangely enough acts only in the immediate neighbourhood of matter. Any force acting on a moving particle changes the velocity, as we already know. I f the net force on the light-corpuscles is an attraction perpendicular to the surface of the glass, the new motion will lie somewhere between the line o f the original path and the perpendicular. This simple explanation seems to promise success for the corpuscular theory of light. To determine the usefulness and range of validity o f the theory, however, we must investigate new and more complicated facts.

其他颜色

T H E R ID D L E O F C O L O U R

牛顿的天才再次首次解释了世界上色彩的丰富性。以下是牛顿亲口对其中一项实验的描述：

It was again Newton’s genius which explained for the first time the wealth o f colour in the world. Here is a description of one of Newton’s experiments in his own words:

1666 年（当时我致力于研磨球面以外的光学玻璃），我弄到了一块三棱玻璃棱镜，用来试验著名的色彩现象。为了做到这一点，

In the year 1666 (at which time I applied myself to the grinding of optick glasses of other figures than spherical) I procured me a triangular glass prism, to try therewith the celebrated phenomena of colours. And in order thereto,

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我把房间弄暗，在窗户上开了一个小洞，让足够数量的阳光照进来，然后把棱镜放在入口处，这样阳光就可以折射到对面的墙上。起初，看到由此产生的鲜艳而强烈的色彩，这是一种非常令人愉快的消遣。

having darkened my chamber, and made a small hole in my window-shuts, to let in a convenient quantity of the sun’s light, I placed my prism at its entrance, that it might thereby be refracted to the opposite wall. It was at first a very pleasing divertisement, to view the vivid and intense colours produced thereby.

太阳发出的光是“白色”的。经过棱镜后，它显示出可见世界中的所有颜色。大自然本身也以彩虹的美丽色彩再现了同样的效果。

The light from the sun is “ white” . After passing through a prism it shows all the colours which exist in the visible world. Nature herself reproduces the same result in the beautiful colour scheme o f the rainbow.

解释这一现象的尝试由来已久。圣经中说彩虹是上帝与人类立约的标志，从某种意义上说，这是一种“理论”。但它无法令人满意地解释为什么彩虹会时不时地出现，以及为什么总是与雨有关。整个色彩之谜首次被科学破解，并在牛顿的伟大著作中指出了答案。

Attempts to explain this phenomenon are very old. The Biblical story that a rainbow is G o d ’s signature to a covenant with man is, in a sense, a “ theory” . But it does not satisfactorily explain why the rainbow is repeated from time to time, and why always in connection with rain. The whole puzzle of colour was first scientifically attacked and the solution pointed out in the great work of Newton.

彩虹的一边总是红色的，另一边总是紫色的。所有其他颜色都排列在它们之间。

O ne edge of the rainbow is always red and the other violet. Between them all other colours are arranged.

牛顿对这一现象的解释是：白光中已经存在每种颜色。它们齐声穿越星际空间和大气层，产生白光的效果。可以说，白光是不同种类、不同颜色的微粒的混合物。在牛顿实验中，棱镜将它们在空间中分离。根据机械理论，折射是由于作用于光粒子的力而产生的，这些力源自玻璃粒子。这些力对于不同的物体来说是不同的

Here is Newton’s explanation o f this phenomenon: every colour is already present in white light. They all traverse interplanetary space and the atmosphere in unison and give the effect o f white light. White light is, so to speak, a mixture o f corpuscles o f different kinds, belonging to different colours. In the case o f Newton’s experiment the prism separates them in space. According to the mechanical theory, refraction is due to forces acting on the particles o f light and originating from the particles of glass. These forces are different for

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不同颜色的粒子，紫色最强，红色最弱。因此，当光线离开棱镜时，每种颜色都会沿着不同的路径折射，并与其他颜色分离。在彩虹中，水滴充当了棱镜的角色。

corpuscles belonging to different colours, being strongest for the violet and weakest for the red. Each of the colours will therefore be refracted along a different path and be separated from the others when the light leaves the prism. In the case o f a rainbow, drops of water play the role o f the prism.

光的物质理论现在比以前更加复杂。我们拥有的不是单一的光物质，而是多种，每种都属于不同的颜色。然而，如果该理论有一定道理，其结果必须与观察结果相符。

The substance theory o f light is now more complicated than before. We have not one light substance but many, each belonging to a different colour. If, however, there is some truth in the theory, its consequences must agree with observation.

牛顿实验揭示的太阳白光中的一系列颜色被称为太阳 光谱，或者更准确地说，是可见光谱。这里描述的白光分解成其成分的过程称为光的色散。除非给出的解释是错误的，否则可以通过适当调整的第二块棱镜将光谱中分离的颜色重新混合在一起。这个过程应该与上一个过程正好相反。我们应该从先前分离的颜色中获得白光。牛顿通过实验表明，确实可以以这种简单的方式多次从其光谱中获得白光，并从白光中获得光谱。这些实验为属于每种颜色的微粒表现为不变物质的理论提供了强有力的支持。牛顿写道：

The series of colours in the white light o f the sun, as revealed by Newton’s experiment, is called the spectrum of the sun, or more precisely, its visible spectrum. The decomposition of white light into its components, as described here, is called the dispersion o f light. The separated colours of the spectrum could be mixed together again by a second prism properly adjusted, unless the explanation given is wrong. The process should be just the reverse o f the previous one. We should obtain white light from the previously separated colours. Newton showed by experiment that it is indeed possible to obtain white light from its spectrum and the spectrum from white light in this simple way as many times as one pleases. These experiments formed a strong support for the theory in which corpuscles belonging to each colour behave as unchangeable substances. Newton wrote thus:

……这些颜色不是新产生的，而只是通过分离才显现出来；因为如果它们再次完全

. . .which colours are not new generated, but only made apparent by being parted; for if they be again entirely

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混合在一起后，它们会重新组成分离前的颜色。出于同样的原因，不同颜色的聚集所产生的变化并不是真实的；因为当不同形状的光线再次分离时，它们会呈现出与进入组合之前完全相同的颜色；正如你所看到的，蓝色和黄色粉末在精细混合后，在肉眼看来是绿色的，然而组成粒子的颜色并没有因此而真正发生变化，而只是混合在一起。因为当用好的显微镜观察时，它们仍然呈现出蓝色和黄色的散布。

mixt and blended together, they will again compose that colour, which they did before separation. And for the same reason, transmutations made by the convening of divers colours are not real; for when the difform rays are again severed, they will exhibit the very same colours which they did before they entered the composition; as you see blue and yellow powders, when finely mixed, appear to the naked eye, green, and yet the colours of the component corpuscles are not thereby really transmuted, but only blended. For when viewed with a good microscope they still appear blue and yellow interspersedly.

假设我们已经分离出一个非常窄的光谱带。这意味着，在众多颜色中，我们只允许一种颜色穿过狭缝，其他颜色被屏幕阻挡。穿过的光束将由同质光组成，也就是说，光不能再分成其他成分。这是理论的结果，可以通过实验轻松证实。这种单一颜色的光束无论如何都不能再进一步分割。有简单的方法可以获得同质光源。例如，钠在白炽状态下会发出同质黄光。用同质光进行某些光学实验通常非常方便，因为正如我们所知，结果会简单得多。

Suppose that we have isolated a very narrow strip of the spectrum. This means that of all the many colours we allow only one to pass through the slit, the others being stopped by a screen. The beam which comes through will consist of homogeneous light, that is, light which cannot be split into further components. This is a consequence o f the theory and can be easily confirmed by experiment. In no way can such a beam o f single colour be divided further. There are simple means of obtaining sources o f homogeneous light. For example, sodium, when incandescent, emits homogeneous yellow light. It is very often convenient to perform certain optical experiments with homogeneous light, since, as we can well understand, the result will be much simpler.

让我们想象一下，突然发生了一件非常奇怪的事情：我们的太阳开始只发出某种特定颜色的同质光，比如黄色。地球上的多种颜色会立即消失。一切都会变成黄色或黑色！

Let us imagine that suddenly a very strange thing happens: our sun begins to emit only homogeneous light of some definite colour, say yellow. The great variety o f colours on the earth would immediately vanish. Everything would be either yellow or black!

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这一预测是光的物质理论的结果，因为新的颜色是无法创造的。它的有效性可以通过实验得到证实：在一个只有白炽钠灯作为唯一光源的房间里，所有的东西要么是黄色，要么是黑色。世界上色彩的丰富性反映了白光所含颜色的多样性。

This prediction is a consequence of the substance theory o f light, for new colours cannot be created. Its validity can be confirmed by experiment: in a room where the only source of light is incandescent sodium everything is either yellow or black. The wealth o f colour in the world reflects the variety o f colour o f which white light is composed.

光的物质理论似乎在所有这些情况下都发挥了出色的作用，尽管引入与颜色一样多的物质的必要性可能会让我们有些不安。假设所有光粒子在空旷的空间中都具有完全相同的速度似乎也很不自然。

The substance theory of light seems to work splendidly in all these cases, although the necessity for introducing as many substances as colours may make us somewhat uneasy. The assumption that all the corpuscles o f light have exactly the same velocity in empty space also seems very artificial.

可以想象，另一组假设，一种性质完全不同的理论，同样可以发挥作用，并给出所有必要的解释。事实上，我们很快就会看到另一种理论的兴起，它基于完全不同的概念，但解释的是同一领域的光学现象。然而，在提出这一新理论的基本假设之前，我们必须回答一个与这些光学考虑无关的问题。我们必须回到力学并问：

It is imaginable that another set o f suppositions, a theory o f entirely different character, would work just as well and give all the required explanations. Indeed, we shall soon witness the rise o f another theory, based on entirely different concepts, yet explaining the same domain of optical phenomena. Before formulating the underlying assumptions of this new theory, however, we must answer a question in no way connected with these optical considerations. We must go back to mechanics and ask:

什么是 AWAVE？

W H A T IS A W A V E ?

从伦敦传出的谣言很快就传到了爱丁堡，尽管没有一个人在这两个城市之间传播谣言。这涉及两种截然不同的动向：谣言从伦敦传到爱丁堡，以及传播谣言的人。

A bit o f gossip starting in London reaches Edinburgh very quickly, even though not a single individual who takes part in spreading it travels between these two cities. There are two quite different motions involved, that o f the rumour, London to Edinburgh, and that o f the persons who spread the rumour. The

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风吹过一片麦田，形成一道波，波及整个麦田。在这里，我们必须再次区分波的运动和单独植物的运动，后者只经历很小的振动。我们都看到过，当一块石头被扔进水池时，波会以越来越宽的圆圈传播开来。波的运动与水粒子的运动截然不同。

wind, passing over a field o f grain, sets up a wave which spreads our across the whole field. Here again we must distinguish between the motion of the wave and the motion o f the separate plants, which undergo only small oscillations. We have all seen the waves that spread in wider and wider circles when a stone is thrown into a pool of water. The motion o f the wave is very different from that of the particles o f water.

粒子只是上下运动。观察到的波浪运动是物质状态的运动，而不是物质本身的运动。漂浮在波浪上的软木塞清楚地表明了这一点，因为它上下移动以模仿水的实际运动，而不是被波浪带走。

The particles merely go up and down. The observed motion of the wave is that of a state of matter and not of matter itself. A cork floating on the wave shows this clearly, for it moves up and down in imitation of the actual motion of the water, instead of being carried along by the wave.

为了更好地理解波的机制，让我们再次考虑一个理想化的实验。

In order to understand better the mechanism o f the wave let us again consider an idealized experiment.

假设一个大空间均匀地充满了水、空气或其他“介质”。中心某处有一个球体。实验开始时，球体没有任何运动。突然，球体开始有节奏地“呼吸”，体积膨胀和收缩，但保持球形。介质中会发生什么？让我们从球体开始膨胀的那一刻开始研究。球体附近的介质粒子被推出，因此水或空气（视情况而定）球壳的密度高于其正常值。同样，当球体收缩时，紧邻它的那部分介质的密度将

Suppose that a large space is filled quite uniformly with water, or air, or some other “ medium” . Somewhere in the centre there is a sphere. A t the beginning of the experiment there is no motion at all. Suddenly the sphere begins to “ breathe” rhythmically, expanding and contracting in volume, although retaining its spherical shape. What will happen in the medium? Let us begin our examination at the moment the sphere begins to expand. The particles of the medium in the immediate vicinity o f the sphere are pushed out, so that the density o f a spherical shell of water, or air, as the case may be, is increased above its normal value. Similarly, when the sphere contracts, the density of that part of the medium immediately surrounding it will be

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减小。这些密度变化会在整个介质中传播。构成介质的粒子只进行小振动，但整个运动是前进波的运动。这里本质上新颖的是，我们第一次考虑不是物质而是通过物质传播的能量的运动。

decreased. These changes o f density are propagated throughout the entire medium. The particles constituting the medium perform only small vibrations, but the whole motion is that of a progressive wave. The essentially new thing here is that for the first time we consider the motion o f something which is not matter, but energy propagated through matter.

以脉动球体为例，我们可以引入两个一般的物理概念，它们对于波的表征很重要。第一个是波传播的速度。这取决于介质，例如，对于水和空气来说，速度是不同的。

Using the example of the pulsating sphere, we may introduce two general physical concepts, important for the characterization o f waves. The first is the velocity with which the wave spreads. This will depend on the medium, being different for water and air, for example.

第二个概念是波长。对于海浪或河浪，波长是从一个波谷到下一个波谷的距离，或从一个波峰到下一个波峰的距离。因此，海浪的波长比河浪大。对于由脉动球体产生的波浪，波长是两个相邻球壳在某个确定时刻的密度最大值或最小值之间的距离。显然，这个距离不仅仅取决于介质。球体的脉动速率肯定会产生很大的影响，如果脉动变得更快，波长就会变短，如果脉动变得更慢，波长就会变长。

The second concept is that o f wave-length. In the case o f waves on a sea or river it is the distance from the trough of one wave to that of the next, or from the crest of one wave to that of the next. Thus sea waves have greater wave-length than river waves. In the case of our waves set up by a pulsating sphere the wave-length is the distance, at some definite time, between two neighbouring spherical shells showing maxima or minima of density. It is evident that this distance will not depend on the medium alone. The rate o f pulsation of the sphere will certainly have a great effect, making the wave-length shorter if the pulsation becomes more rapid, longer if the pulsation becomes slower.

波的概念在物理学中非常成功。它绝对是一个机械概念。这种现象被归结为粒子的运动，根据动能论，粒子是物质的组成部分。

This concept of a wave proved very successful in physics. It is definitely a mechanical concept. The phenomenon is reduced to the motion of particles which, according to the kinetic theory, are constituents o f

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物质。因此，一般来说，任何使用波概念的理论都可以被视为一种机械理论。例如，对声学现象的解释基本上就是基于这一概念。振动体，如声带和小提琴弦，是声波的来源，声波以脉动球体所解释的方式在空气中传播。

matter. Thus every theory which uses the concept o f wave can, in general, be regarded as a mechanical theory. For example, the explanation o f acoustical phenomena is based essentially on this concept. Vibrating bodies, such as vocal cords and violin strings, are sources of sound waves which are propagated through the air in the manner explained for the pulsating sphere.

因此，可以通过波的概念将所有声学现象归结为力学。

It is thus possible to reduce all acoustical phenomena to mechanics by means o f the wave concept.

已经强调过，我们必须区分粒子的运动和波本身的运动，波是介质的一种状态。两者非常不同，但很明显，在我们的脉动球体示例中，两种运动都发生在同一直线上。介质的粒子沿短线段振荡，密度根据这种运动周期性地增加和减少。

It has been emphasized that we must distinguish between the motion o f the particles and that of the wave itself, which is a state o f the medium. The two are very different, but it is apparent that in our example of the pulsating sphere both motions take place in the same straight line. The particles o f the medium oscillate along short line segments, and the density increases and decreases periodically in accordance with this motion.

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波传播的方向和振动所在的线是相同的。这种波称为纵波。但这是唯一一种波吗？为了进一步考虑，重要的是认识到存在另一种波的可能性，即横波。

The direction in which the wave spreads and the line on which the oscillations lie are the same. This type of wave is called longitudinal. But is this the only kind of wave? It is important for our further considerations to realize the possibility o f a different kind of wave, called transverse.

让我们改变之前的例子。我们仍然有球体，但它浸没在另一种介质中，一种果冻而不是空气或水。此外，球体不再脉动，而是沿一个方向旋转一个小角度，然后再转回来，始终以相同的节奏方式围绕一个确定的轴旋转。果冻粘附在球体上，因此粘附部分被迫模仿运动。

Let us change our previous example. We still have the sphere, but it is immersed in a medium of a different kind, a sort of jelly instead of air or water. Furthermore, the sphere no longer pulsates but rotates in one direction through a small angle and then back again, always in the same rhythmical way and about a definite axis. The jelly adheres to the sphere and thus the adhering portions are forced to imitate the motion.

这些部分迫使那些位于稍远的地方的人模仿相同的运动，依此类推，这样就在介质中建立了波。如果我们记住区别

These portions force those situated a little farther away to imitate the same motion, and so on, so that a wave is set up in the medium. I f we keep in mind the distinction

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在介质运动和波运动之间，我们发现它们不在同一条线上。波沿球体半径方向传播，而介质各部分则垂直于此方向移动。因此，我们创建了横波。

between the motion of the medium and the motion of the wave, we see that here they do not lie on the same line. The wave is propagated in the direction o f the radius o f the sphere, while the parts o f the medium move perpendicularly to this direction. We have thus created a transverse wave.

在水面上传播的波是横向的。漂浮的软木塞只会上下摆动，但波会沿着水平面传播。另一方面，声波则是纵波最常见的例子。

Waves spreading on the surface of water are transverse. A floating cork only bobs up and down, but the wave spreads along a horizontal plane. Sound waves, on the other hand, furnish the most familiar example of longitudinal waves.

再说一句：均匀介质中脉动或振荡球体产生的波是球面波。之所以这样称呼，是因为在任何给定时刻，围绕源的任何球体上的所有点都以相同的方式运动。让我们考虑距离源很远的球体的一部分。这部分距离越远，我们选择的面积越小，它就越像一个平面。我们可以说，虽然不太严格，但平面的一部分和平面的一部分之间没有本质区别

O ne more remark : the wave produced by a pulsating or oscillating sphere in a homogeneous medium is a spherical wave. It is called so because at any given moment all points on any sphere surrounding the source behave in the same way. Let us consider a portion of such a sphere at a great distance from the source. The farther away the portion is, and the smaller we choose to take it, the more it resembles a plane. We can say, without trying to be too rigorous, that there is no essential difference between a part of a plane and

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球体的半径足够大的一部分。

a part of a sphere whose radius is sufficiently large.

我们经常将远离源头的球面波的一小部分称为 平面波。我们画的阴影部分距离球面中心越远，两个半径之间的角度越小，平面波的表示就越准确。平面波的概念与许多其他物理概念一样，只不过是一种虚构，只能以一定的准确度来实现。

We very often speak o f small portions o f a spherical wave far removed from the source as plane waves. The farther we place the shaded portion o f our drawing from the centre of the spheres and the smaller the angle between the two radii, the better our representation of a plane wave. The concept o f a plane wave, like many other physical concepts, is no more than a fiction which can be realized with only a certain degree of accuracy.

然而，这是一个有用的概念，我们以后会需要它。

It is, however, a useful concept which we shall need later.

光的波动说

T H E W A V E T H E O R Y O F L I G H T

让我们回想一下为什么我们中断了对光学现象的描述。我们的目的是引入另一种光理论，它不同于粒子理论，但也试图解释同一领域的事实。

Let us recall why we broke off the description o f optical phenomena. O ur aim was to introduce another theory of light, different from the corpuscular one, but also attempting to explain the same domain of facts.

为此，我们不得不中断故事，介绍一下波浪的概念。现在我们可以回到正题上。

To do this we had to interrupt our story and introduce the concept of waves. Now we can return to our subject.

与牛顿同时代的人惠更斯提出了一个相当新的理论。他在关于光的论文中写道：

It was Huygens, a contemporary o f Newton, who put forward quite a new theory. In his treatise on light he wrote:

此外，如果光需要时间才能通过——我们现在将对此进行研究——那么，这种运动在中间物质上的印象将是连续的；因此，它像声音一样，通过球面和波传播，我称它们为波，是因为它们类似于石头扔进水中时在水中形成的波，它们呈现出连续的

If, in addition, light takes time for its passage—which we are now going to examine—it will follow that this movement, impressed on the intervening matter, is successive; and consequently it spreads, as sound does, by spherical surfaces and waves, for I call them waves from their resemblance to those which are seen to be formed in water when a stone is thrown into it, and which present a successive

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以圆圈形式扩散，尽管这些圆圈是由其他原因引起的，并且仅出现在平面上。

spreading as circles, though these arise from another cause, and are only in a flat surface.

惠更斯认为光是波，是能量的传递，而不是物质的传递。我们已经看到，微粒理论解释了许多观察到的事实。

According to Huygens, light is a wave, a transference of energy and not of substance. We have seen that the corpuscular theory explains many of the observed facts.

波动理论也能做到这一点吗？我们必须再次提出粒子理论已经回答过的问题，看看波动理论是否也能同样出色地回答。我们将以 N 和N之间的对话的形式来做到这一点

Is the wave theory also able to do this? We must again ask the questions which have already been answered by the corpuscular theory, to see whether the wave theory can do the answering just as well. We shall do this here in the form of a dialogue between N

其中 N 是牛顿粒子理论的信徒，而 H是惠更斯理论的信徒。两者都不允许使用两位大师在工作完成后提出的论据。

and H where N is a believer in Newton’s corpuscular theory, and H in Huygen’s theory. Neither is allowed to use arguments developed after the work o f the two great masters was finished.

JV. 在粒子理论中，光速具有非常明确的含义。它是粒子穿过空旷空间的速度。它在波动理论中意味着什么？

JV. In the corpuscular theory the velocity o f light has a very definite meaning. It is the velocity at which the corpuscles travel through empty space. What does it mean in the wave theory?

H。当然是指光波的速度。

H . It means the velocity of the light wave, of course.

每种已知的波都以一定的速度传播，光波也应如此。

Every known wave spreads with some definite velocity, and so should a wave of light.

JV：这并不像看上去那么简单。声波在空气中传播，海浪在水中传播。每一种波都必须有它在其中传播的物质介质。但光可以穿过真空，而声音则不能。假设空旷空间中有波，实际上意味着根本不假设任何波。

JV. That is not as simple as it seems. Sound waves spread in air, ocean waves in water. Every wave must have a material medium in which it travels. But light passes through a vacuum, whereas sound does not. To assume a wave in empty space really means not to assume any wave at all.

是的，这是一个难题，尽管对我来说并不是什么新问题。我的主人仔细思考了一下，决定唯一的出路就是假设存在

H . Yes, that is a difficulty, although not a new one to me. M y master thought about it very carefully, and decided that the only way out is to assume the existence

假设物质 1

of a hypothetical substan 1

ce，以太，透明的

ce, the ether, a transparent

以太是弥漫整个宇宙的介质。可以说，宇宙沉浸在以太之中。一旦我们有勇气引入这个概念，其他一切都会变得清晰和令人信服。

medium permeating the entire universe. The universe is, so to speak, immersed in ether. Once we have the courage to introduce this concept, everything else becomes clear and convincing.

N。但我反对这种假设。首先，它引入了一种新的假设物质，而物理学中已经有太多物质了。反对它还有另一个理由。你无疑认为我们必须用力学来解释一切。

N . But I object to such an assumption. In the first place it introduces a new hypothetical substance, and we already have too many substances in physics. There is also another reason against it. You no doubt believe that we must explain everything in terms of mechanics.

但以太又如何呢？你能回答这个简单的问题吗：以太是如何由其基本粒子构成的，以及它如何在其他现象中显现出来？

But what about the ether? Are you able to answer the simple question as to how the ether is constructed from its elementary particles and how it reveals itself in other phenomena?

H.你的第一个反对意见当然是有道理的。但是，通过引入某种程度上是人造的无重量以太，我们立刻就摆脱了更加人造的光粒子。我们只有一种“神秘”的物质，而不是与光谱中大量颜色相对应的无数种物质。你不认为这是真正的进步吗？至少所有的困难都集中在一点上。我们不再需要人为的假设，即不同颜色的粒子以相同的速度穿过空的空间。你的第二个论点也是正确的。我们无法对以太做出机械解释。但毫无疑问，未来对光学和其他现象的研究将揭示其结构。目前我们必须等待新的实验和结论，但最终，我希望，我们将

H . Your first objection is certainly justified. But by introducing the somewhat artificial weightless ether we at once get rid of the much more artificial light corpuscles. We have only one “ mysterious” substance instead of an infinite number o f them corresponding to the great number o f colours in the spectrum. D o you not think that this is real progress? A t least all the difficulties are concentrated on one point. We no longer need the factitious assumption that particles belonging to different colours travel with the same speed through empty space. Your second argument is also true. We cannot give a mechanical explanation of ether. But there is no doubt that the future study of optical and perhaps other phenomena will reveal its structure. A t present we must wait for new experiments and conclusions, but finally, I hope, we shall be

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能够澄清以太的机械结构问题。

able to clear up the problem of the mechanical structure o f the ether.

N：我们先把这个问题搁置一边，因为现在还不能解决。我想看看，即使我们放弃这些困难，你的理论如何解释那些根据粒子理论可以如此清晰和理解的现象。举个例子，光线 在真空 或空气中沿直线传播。放在蜡烛前面的一张纸会在墙上产生清晰而轮廓分明的阴影。如果光的波动理论是正确的，那么就不可能出现清晰的阴影，因为波会绕着纸的边缘弯曲，从而使阴影变得模糊。你知道，小船不会成为海上波浪的障碍；它们只是绕着它弯曲，不会投下阴影。

N . Let us leave the question for the moment, since it cannot be settled now. I should like to see how your theory, even if we waive the difficulties, explains those phenomena which are so clear and understandable in the light of the corpuscular theory. Take, for example, the fact that light rays travel in vacuo or in air along straight lines. A piece of paper placed in front of a candle produces a distinct and sharply outlined shadow on the wall. Sharp shadows would not be possible if the wave theory of light were correct, for waves would bend around the edges of the paper and thus blur the shadow. A small ship is not an obstacle for waves on the sea, you know; they simply bend around it without casting a shadow.

H 。T 这不是一个令人信服的论点。以河流上的短波冲击一艘大船的侧面为例。

H . T hat is not a convincing argument. Take short waves on a river impinging on the side of a large ship.

船一侧的波浪在另一侧是看不见的。如果波浪足够小而船足够大，就会出现非常明显的阴影。

Waves originating on one side of the ship will not be seen on the other. I f the waves are small enough and the ship large enough, a very distinct shadow appears.

光似乎沿直线传播，很可能只是因为其波长与普通障碍物和实验中使用的孔径相比非常小。也许，如果我们能制造出足够小的障碍物，就不会出现阴影。在构造能够显示光是否能够弯曲的仪器时，我们可能会遇到巨大的实验困难。然而，如果能设计出这样的实验，这将是至关重要的

It is very probable that light seems to travel in straight lines only because its wave-length is very small in comparison with the size of ordinary obstacles and of apertures used in experiments. Possibly, if we could create a sufficiently small obstruction, no shadow would occur. We might meet with great experimental difficulties in constructing apparatus which would show whether light is capable of bending. Nevertheless, if such an experiment could be devised it would be crucial

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在光的波动说和粒子说之间做出选择。

in deciding between the wave theory and the corpuscular theory of light.

N 波动理论将来可能会带来新的事实，但我不知道有任何实验数据可以令人信服地证实这一点。除非实验明确证明光可以弯曲，否则我看不出有任何理由不相信粒子理论，在我看来，粒子理论比波动理论更简单，因此也更好。

N . The wave theory may lead to new facts in the future, but I do not know o f any experimental data confirming it convincingly. U n til it is definitely proved by experiment that light may be bent, I do not see any reason for not believing in the corpuscular theory, which seems to me to be simpler, and therefore better, than the wave theory.

此时我们可以打断对话，尽管这个话题还远远没有结束。

A t this point we may interrupt the dialogue, though the subject is by no means exhausted.

波动理论如何解释光的折射和颜色的多样性仍有待阐明。

It still remains to be shown how the wave theory explains the refraction of light and the variety of colours.

我们知道，微粒理论能够做到这一点。

The corpuscular theory is capable of this, as we know.

我们将从折射开始，但首先考虑一个与光学无关的例子会很有用。

We shall begin with refraction, but it will be useful to consider first an example having nothing to do with optics.

那里有一块很大的空地，里面走着两个男人，他们中间握着一根坚硬的杆子。

There is a large open space in which there are walking two men holding between them a rigid pole.

一开始，他们径直向前行走，速度相同。只要他们的速度相同，无论速度大还是小，棍子都会发生平行位移；也就是说，它不会转动或改变方向。杆子的所有连续位置都是平行的。但现在想象一下，在短短几分之一秒的时间内，这两个人的运动并不相同。

A t the beginning they are walking straight ahead, both with the same velocity. As long as their velocities remain the same, whether great or small, the stick will be undergoing parallel displacement; that is, it does not turn or change its direction. A ll consecutive positions o f the pole are parallel to each other. But now imagine that for a time which may be as short as a fraction of a second the motions of the two men are not the same.

会发生什么？很明显，此时棍子会转动，因此它不再平行于其原始位置。当速度相等时

What will happen? It is clear that during this moment the stick will turn, so that it will no longer be displaced parallel to its original position. When the equal velocities

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恢复时，方向与之前不同。这在图中显示得很清楚。

are resumed, it is in a direction different from the previous one. This is shown clearly in the drawing.

方向的改变发生在两位步行者速度不同的时间间隔内。

The change in direction took place during the time interval in which the velocities of the two walkers were different.

这个例子将使我们理解波的折射。穿过以太的平面波撞击玻璃板。在下图中，我们看到波在行进时呈现出相对较宽的波前。波前是一个平面，在任何给定时刻，以太的所有部分都以完全相同的方式表现。由于速度取决于光穿过的介质，因此它在玻璃中的速度与在真空中的速度不同。

This example will enable us to understand the refraction o f a wave. A plane wave travelling through the ether strikes a plate of glass. In the next drawing we see a wave which presents a comparatively wide front as it marches along. The wave front is a plane on which at any given moment all parts o f the ether behave in precisely the same way. Since the velocity depends on the medium through which the light is passing, it will be different in glass from the velocity in empty space.

在波阵面进入玻璃的极短时间内，波阵面的不同部分将具有不同的速度。很明显，到达玻璃的部分将以光在玻璃中的速度行进，而另一部分仍以光在以太中的速度移动。由于这种速度差异

During the very short time in which the wave front enters the glass, different parts o f the wave front will have different velocities. It is clear that the part which has reached the glass will travel with the velocity o f light in glass, while the other still moves with the velocity of light in ether. Because of this difference in velocity

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在“浸没”期间沿着波前

along the wave front during the time of “ immersion”

在玻璃中，波本身的方向将是因此，我们看到，不仅粒子理论，而且波动理论，都导致了折射的解释。进一步的考虑，再加上一点数学知识，表明波动理论的解释更简单、更好，而且结果与观察结果完全一致。事实上，如果我们知道光束在进入折射介质时如何折射，定量推理方法使我们能够推断出光在折射介质中的速度。直接测量出色地证实了这些预测，从而也证实了光的波动理论。

in the glass, the direction o f the wave itself will be Thus we see that not only the corpuscular theory, but also the wave theory, leads to an explanation of refraction. Further consideration, together with a little mathematics, shows that the wave theory explanation is simpler and better, and that the consequences are in perfect agreement with observation. Indeed, quantitative methods of reasoning enable us to deduce the velocity of light in a refractive medium if we know how the beam refracts when passing into it. Direct measurements splendidly confirm these predictions, and thus also the wave theory of light.

颜色问题仍然存在。

There still remains the question o f colour.

必须记住，波的特征有两个：速度和波长。光波动理论的基本假设是，不同的波长对应不同的颜色。

It must be remembered that a wave is characterized by two numbers, its velocity and its wave-length. The essential assumption o f the wave theory o f light is that different wave-lengths correspond to different colours. The

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均匀黄光的波长与红光或紫光的波长不同。我们不用人为地将不同颜色的粒子分开，而是采用自然的波长差异。

wave-length o f homogeneous yellow light differs from that of red or violet. Instead of the artificial segregation of corpuscles belonging to various colours we have the natural difference in wave-length.

因此，牛顿关于光的色散实验可以用两种不同的语言来描述，即粒子理论和波动理论。

It follows that Newton’s experiments on the dispersion of light can be described in two different languages, that o f the corpuscular theory and that of the wave theory.

例如：

For exam ple:

微粒语言

C orpuscular L a n gu a ge

波浪语言

W a ve L an gu a ge

属于

The corpuscles belonging

不同波浪的光芒

The rays of different wave

不同颜色有

to different colours have the

长度属于不同相同的真空速度，但 颜色具有相同的

length belonging to differsame velocity in vacuo, but ent colours have the same

玻璃中的不同速度。

different velocities in glass.

以太中的速度，但是

velocity in the ether, but

玻璃中的不同速度。

different velocities in glass.

白光是一种合成光

White light is a composi

白光是由属于 不同颜色、不同 长度的波的微粒组成的，而在光谱的规格中它们是 分开的。

White light is a composition of corpuscles belonging tion of waves of all waveto different colours, whereas lengths, whereas in the specin the spectrum they are trum they are separated.

分开。

separated.

明智的做法是，在仔细考虑每种理论的优点和缺点之后，决定采用其中一种理论，这样可以避免因同一现象存在两种不同理论而产生的歧义。

It would seem wise to avoid the ambiguity resulting from the existence of two distinct theories of the same phenomena, by deciding in favour o f one of them after a careful consideration o f the faults and merits o f each.

N 和 H之间的对话表明，这并非易事。此时做出决定更多的是个人喜好问题，而非科学信念问题。在牛顿时代以及之后的一百多年里，大多数物理学家都支持粒子理论。

The dialogue between N and H shows that this is no easy task. The decision at this point would be more a matter of taste than of scientific conviction. In Newton’s time, and for more than a hundred years after, most physicists favoured the corpuscular theory.

历史做出了有利于光的波动说、反对粒子说的判决。

History brought in its verdict, in favour of the wave theory of light and against the corpuscular theory, at

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更晚的日期，即十九世纪中叶。在与 H 的对话中，N 表示，从原则上来说，在两种理论之间做出决定是可能的。粒子理论不允许光弯曲，并且要求存在清晰的阴影。另一方面，根据波动理论，足够小的障碍物不会投射阴影。在杨和菲涅尔的工作中，这个结果通过实验实现，并得出了理论结论。

a much later date, the middle o f the nineteenth century. In his conversation with H , N stated that a decision between the two theories was, in principle, experimentally possible. The corpuscular theory does not allow light to bend, and demands the existence of sharp shadows. According to the wave theory, on the other hand, a sufficiently small obstacle will cast no shadow. In the work of Young and Fresnel this result was experimentally realized and theoretical conclusions were drawn.

我们已经讨论过一个非常简单的实验，其中一块带孔的屏幕被放置在点光源前，并且墙上出现了一个阴影。我们将进一步简化实验，假设光源发出的是均匀光。

A n extremely simple experiment has already been discussed, in which a screen with a hole was placed in front of a point source of light and a shadow appeared on the wall. We shall simplify the experiment further by assuming that the source emits homogeneous light.

为了获得最佳效果，信号源应该是强大的。

For the best results the source should be a strong one.

让我们想象一下，屏幕上的洞越来越小。如果我们使用强光源并成功地使洞足够小，就会出现一种新的、令人惊奇的现象，从粒子理论的角度来看，这是完全无法理解的。光与暗之间不再有明显的界限。光在一系列明暗环中逐渐消失在黑暗的背景中。

Let us imagine that the hole in the screen is made smaller and smaller. I f we use a strong source and succeed in making the hole small enough, a new and surprising phenomenon appears, something quite incomprehensible from the point o f view o f the corpuscular theory. There is no longer a sharp distinction between light and dark. Light gradually fades into the dark background in a series o f light and dark rings.

环的出现是波动理论的一个典型特征。如果采用稍微不同的实验布置，明暗交替区域的解释就会变得清晰。假设我们有一张深色纸，上面有两个针孔，光线可以通过。如果两个孔靠得很近，而且非常

The appearance of rings is very characteristic o f a wave theory. The explanation for alternating light and dark areas will be clear in the case o f a somewhat different experimental arrangement. Suppose we have a sheet of dark paper with two pinholes through which light may pass. I f the holes are close together and very

图二

P L A T E II

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光的波长很小，如果均匀光源足够强，墙上就会出现许多明暗带，在侧面逐渐消失在黑暗的背景中。解释很简单。暗带是指一个针孔发出的波的波谷与另一个针孔发出的波峰相遇，从而相互抵消。光带是指不同针孔发出的波的两个波谷或两个波峰相遇并相互加强。对于我们之前使用一个孔的屏幕的例子中出现的暗环和亮环，解释起来更加复杂，但原理是一样的。应该记住这种在两个孔的情况下出现的暗带和亮环，以及在只有一个孔的情况下出现的亮环和暗环，因为我们稍后会回到对这两幅不同图片的讨论。这里描述的实验显示了光的衍射，即当小孔或障碍物挡住光波的路径时，光会偏离直线传播。

small, and if the source o f homogeneous light is strong enough, many light and dark bands will appear on the wall, gradually fading off at the sides into the dark background. The explanation is simple. A dark band is where a trough o f a wave from one pinhole meets the crest o f a wave from the other pinhole, so that the two cancel. A band o f light is where two troughs or two crests from waves of the different pinholes meet and reinforce each other. T he explanation is more complicated in the case of the dark and light rings o f our previous example in which we used a screen with one hole, but the principle is the same. This appearance of dark and light stripes in the case o f two holes and of light and dark rings in the case o f one hole should be borne in mind, for we shall later return to a discussion of the two different pictures. The experiments described here show the diffraction of light, the deviation from the rectilinear propagation when small holes or obstacles are placed in the way of the light wave.

借助一点数学知识，我们可以走得更远。我们可以找出波长必须有多大，或者说多小才能产生特定的图案。因此，所描述的实验使我们能够测量用作光源的均匀光的波长。为了说明这些数字有多小，我们将引用两个波长，它们代表太阳光谱的极端值，即红色和紫色。

With the aid of a little mathematics we are able to go much further. It is possible to find out how great or, rather, how small the wave-length must be to produce a particular pattern. Thus the experiments described enable us to measure the wave-length of the homogeneous light used as a source. To give an idea of how small the numbers are we shall cite two wavelengths, those representing the extremes o f the solar spectrum, that is, the red and the violet.

红光的波长为0.00008厘米。

The wave-length o f red light is 0.00008 cm.

紫光的波长是0.00004厘米。

The wave-length of violet light is 0.00004 cm.

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我们不应该对数字如此之小感到惊讶。自然界中观察到明显阴影的现象，即光的直线传播现象，只是因为通常遇到的所有孔径和障碍物与光的波长相比都非常大。只有当使用非常小的障碍物和孔径时，光才会显示出其波状性质。

We should not be astonished that the numbers are so small. The phenomenon of distinct shadow, that is, the phenomenon of rectilinear propagation of light, is observed in nature only because all apertures and obstacles ordinarily met with are extremely large in comparison with the wave-lengths of light. It is only when very small obstacles and apertures are used that light reveals its wave-like nature.

但寻找光理论的故事绝不会结束。十九世纪的裁决并非最终的。对于现代物理学家来说，在粒子和波之间做出抉择的整个问题再次存在，这一次是以更加深刻和复杂的形式。让我们接受光粒子理论的失败，直到我们认识到波动理论胜利的本质问题。

But the story of the search for a theory o f light is by no means finished. The verdict o f the nineteenth century was not final and ultimate. For the modern physicist the entire problem of deciding between corpuscles and waves again exists, this time in a much more profound and intricate form. Let us accept the defeat o f the corpuscular theory of light until we recognize the problematic nature of the victory of the wave theory.

纵向或横向 RS 光波？

L O N G I T U D I N A L O R T R A N S V E R S E L I G H T W A V E S ?

我们所考虑的所有光学现象都支持波动理论。光绕过小障碍物时的弯曲和折射的解释是支持波动理论的最有力论据。在机械观点的指导下，我们意识到还有一个问题需要回答：以太的机械性质的确定。要解决这个问题，必须知道以太中的光波是纵向的还是横向的。换句话说：光像声音一样传播吗？波是否由于介质密度的变化而产生，因此粒子的振动方向是

A ll the optical phenomena we have considered speak for the wave theory. The bending of light around small obstacles and the explanation o f refraction are the strongest arguments in its favour. Guided by the mechanical point o f view we realize that there is still one question to be answered: the determination o f the mechanical properties of the ether. It is essential for the solution of this problem to know whether light waves in the ether are longitudinal or transverse. In other words: is light propagated like sound? Is the wave due to changes in the density of the medium, so that the oscillations of the particles are in the direction of the

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传播？或者以太就像一种弹性果冻，一种只能产生横波的介质，其粒子的运动方向垂直于波本身的传播方向？

propagation? O r does the ether resemble an elastic jelly, a medium in which only transverse waves can be set up and whose particles move in a direction perpendicular to that in which the wave itself travels?

在解决这个问题之前，让我们先决定应该选择哪个答案。显然，如果光波是纵向的，那我们就很幸运了。

Before solving this problem, let us try to decide which answer should be preferred. Obviously, we should be fortunate if light waves were longitudinal.

在这种情况下，设计机械以太的困难就会简单得多。我们对以太的描述很可能类似于解释声波传播的气体的机械描述。而要描述携带横波的以太则要困难得多。要把果冻想象成一种由粒子组成的介质，让横波通过它传播，这绝非易事。惠更斯认为，以太最终会是“像空气”而不是“像果冻”。但大自然并不关心我们的局限性。在这种情况下，大自然会怜悯那些试图从机械观点理解所有事件的物理学家吗？

The difficulties in designing a mechanical ether would be much simpler in this case. O ur picture o f ether might very probably be something like the mechanical picture of a gas that explains the propagation of sound waves. It would be much more difficult to form a picture of ether carrying transverse waves. To imagine a jelly as a medium made up of particles in such a way that transverse waves are propagated by means of it is no easy task. Huygens believed that the ether would turn out to be “ air-like” rather than “ jelly-like” . But nature cares very little for our limitations. Was nature, in this case, merciful to the physicists attempting to understand all events from a mechanical point o f view?

为了回答这个问题，我们必须讨论一些新的实验。

In order to answer this question we must discuss some new experiments.

我们将详细考虑众多能够为我们提供答案的实验中的一个。

We shall consider in detail only one of many experiments which are able to supply us with an answer.

假设我们有一块非常薄的电气石晶体板，它以一种特殊的方式切割而成，我们在这里就不多说了。这块晶体板必须很薄，这样我们才能透过它看到光源。但现在让我们拿两块这样的板，把它们都放在我们的眼睛和光源之间。我们期望看到什么呢？

Suppose we have a very thin plate of tourmaline crystal, cut in a particular way which we need not describe here. The crystal plate must be thin so that we are able to see a source o f light through it. But now let us take two such plates and place both o f them between our eyes and the light. What do we expect to

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看到了吗？如果薄片足够薄，那么又是一个光点。实验很有可能证实我们的预期。不必担心这可能是偶然的说法，让我们假设我们确实透过两块晶体看到了光点。现在让我们通过旋转其中一块晶体来逐渐改变它的位置。只有旋转轴的位置固定时，这种说法才有意义。我们将以入射光线确定的线为轴。这意味着我们将一块晶体上除轴上的点以外的所有点都移位。奇怪的事情发生了！光越来越弱，直到完全消失。随着旋转的继续，光会重新出现，当到达初始位置时，我们会重新获得初始视图。

see? Again a point o f light, if the plates are sufficiently thin. The chances are very good that the experiment will confirm our expectation. Without worrying about the statement that it may be chance, let us assume we do see the light point through the two crystals. Now let us gradually change the position of one of the crystals by rotating it. This statement makes sense only if the position of the axis about which the rotation takes place is fixed. We shall take as an axis the line determined by the incoming ray. This means that we displace all the points of the one crystal except those on the axis. A strange thing happens ! The light gets weaker and weaker until it vanishes completely. It reappears as the rotation continues and we regain the initial view when the initial position is reached.

不去深入讨论这个和类似的事情

Without going into the details o f this and similar

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实验中，我们可以提出以下问题：如果光波是纵向的，这些现象能得到解释吗？在纵向波的情况下，以太粒子会像光束一样沿轴移动。如果晶体旋转，轴上没有任何变化。轴上的点不会移动，附近只会发生非常小的位移。对于纵向波，不可能出现像消失和出现新图像这样明显的变化。这种现象和许多其他类似现象只能通过假设光波是横向的而不是纵向的来解释！或者，换句话说，必须假设以太具有“果冻状”的特性。

experiments we can ask the following question: can these phenomena be explained if the light waves are longitudinal? In the case of longitudinal waves the particles o f the ether would move along the axis, as the beam does. I f the crystal rotates, nothing along the axis changes. The points on the axis do not move, and only a very small displacement takes place nearby. No such distinct change as the vanishing and appearance o f a new picture could possibly occur for a longitudinal wave. This and many other similar phenomena can be explained only by the assumption that light waves are transverse and not longitudinal! O r, in other words, the “ jelly-like” character o f the ether must be assumed.

这太可悲了！我们必须做好面对巨大困难的准备，才能用机械的方式描述以太。

This is very s a d ! We must be prepared to face tremendous difficulties in the attempt to describe the ether mechanically.

以太与机械观

E T H E R A N D T H E M E C H A N I C A L V I E W

讨论所有试图理解以太作为光传输介质的机械性质的各种尝试，将会是一个很长的故事。众所周知，机械构造意味着物质是由粒子构成的，力沿着连接它们的线作用，并且只取决于距离。为了将以太构造成一种果冻状的机械物质，物理学家必须做出一些非常人为和不自然的假设。我们不会在这里引用它们；它们属于几乎被遗忘的过去。但结果是意义重大的。所有这些假设的人为性质，

The discussion o f all the various attempts to understand the mechanical nature o f the ether as a medium for transmitting light would make a long story. A mechanical construction means, as we know, that the substance is built up o f particles with forces acting along lines connecting them and depending only on the distance. In order to construct the ether as a jelly-like mechanical substance physicists had to make some highly artificial and unnatural assumptions. We shall not quote them here; they belong to the almost forgotten past. But the result was significant and important. The artificial character o f all these assumptions,

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引入如此多彼此独立的因素的必要性足以粉碎人们对机械观点的信念。

the necessity for introducing so many of them all quite independent o f each other, was enough to shatter the belief in the mechanical point of view.

但是，除了构造以太的难度之外，还有其他更简单的反对理由。如果我们想用机械的方式解释光学现象，就必须假设以太无处不在。如果光只在介质中传播，就不可能存在真空。

But there are other and simpler objections to ether than the difficulty of constructing it. Ether must be assumed to exist everywhere, if we wish to explain optical phenomena mechanically. There can be no empty space if light travels only in a medium.

然而，根据力学原理，星际空间并不阻碍物质运动。例如，行星在以太胶冻中穿行时，不会遇到任何物质介质对其运动产生的阻力。如果以太不干扰物质的运动，以太粒子和物质粒子之间就不会发生相互作用。光可以穿过以太，也可以穿过玻璃和水，但光在后一种物质中的速度会发生变化。如何用力学方法解释这一事实？显然，只有假设以太粒子和物质粒子之间存在某种相互作用。我们刚刚看到，在自由运动的物体的情况下，必须假设不存在这种相互作用。换句话说，在光学现象中存在以太和物质之间的相互作用，但在机械现象中却不存在相互作用！这当然是一个非常矛盾的结论！

Yet we know from mechanics that interstellar space does not resist the motion o f material bodies. The planets, for example, travel through the ether-jelly without encountering any resistance such as a material medium would offer to their motion. I f ether does not disturb matter in its motion, there can be no interaction between particles of ether and particles o f matter. Light passes through ether and also through glass and water, but its velocity is changed in the latter substances. How can this fact be explained mechanically? Apparently only by assuming some interaction between ether particles and matter particles. We have just seen that in the case o f freely moving bodies such interactions must be assumed not to exist. In other words, there is interaction between ether and matter in optical phenomena, but none in mechanical phenom ena! This is certainly a very paradoxical conclusion !

解决所有这些困难的方法似乎只有一个。在试图从机械观点理解自然现象的过程中，在整个科学发展过程中，直到二十世纪，都必须引入

There seems to be only one way out of all these difficulties. In the attempt to understand the phenomena o f nature from the mechanical point o f view, throughout the whole development o f science up to the twentieth century, it was necessary to introduce

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人造物质，如电和磁流体、光微粒或以太。结果只是将所有困难集中在几个基本点上，例如光学现象中的以太。

artificial substances like electric and magnetic fluids, light corpuscles, or ether. The result was merely the concentration of all the difficulties in a few essential points, such as ether in the case of optical phenomena.

这里，所有试图以某种简单方式构造以太的徒劳尝试以及其他反对意见似乎都表明，错误在于基本假设，即可以从机械的角度解释自然界的所有事件。科学未能令人信服地实施机械计划，今天没有物理学家相信它能够实现。

Here all the fruitless attempts to construct an ether in some simple way, as well as the other objections, seem to indicate that the fault lies in the fundamental assumption that it is possible to explain all events in nature from a mechanical point of view. Science did not succeed in carrying out the mechanical programme convincingly, and today no physicist believes in the possibility of its fulfilment.

在我们对主要物理思想的简短回顾中，我们遇到了一些未解决的问题，遇到了一些困难和障碍，这些困难和障碍阻碍了我们试图形成统一一致的观点来看待外部世界的所有现象。经典力学中有一个未被注意到的线索，即引力和惯性质量相等。还有电流体和磁流体的人工特性。

In our short review o f the principal physical ideas we have met some unsolved problems, have come upon difficulties and obstacles which discouraged the attempts to formulate a uniform and consistent view of all the phenomena of the external world. There was the unnoticed clue in classical mechanics of the equality of gravitational and inertial mass. There was the artificial character of the electric and magnetic fluids.

电流与磁针的相互作用中，有一个尚未解决的难题。大家还记得，这种力并不作用于连接导线和磁极的线上，而是取决于移动电荷的速度。表达其方向和大小的定律极其复杂。

There was, in the interaction between electric current and magnetic needle, an unsolved difficulty. It will be remembered that this force did not act in the line connecting the wire and the magnetic pole, and depended on the velocity of the moving charge. The law expressing its direction and magnitude was extremely complicated.

最后，以太存在很大的困难。

And finally, there was the great difficulty with the ether.

现代物理学已经攻克了所有这些问题，并解决了它们。但在寻求这些解决方案的过程中

Modern physics has attacked all these problems and solved them. But in the struggle for these solutions

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新的、更深刻的问题出现了。我们的知识比十九世纪的物理学家更广泛、更深刻，但我们的疑虑和困难也同样如此。

new and deeper problems have been created. O ur knowledge is now wider and more profound than that of the physicist of the nineteenth century, but so are our doubts and difficulties.

我们总结一下：

W e S u m m a r iz e :

在古老的电流体理论、光的粒子 和波动理论中，我们见证了应用机械观点的进一步尝试 。但在电和光现象领域， 我们在 应用这一观点时遇到了严重困难。

In the old theories o f electric fluids, in the corpuscular and wave theories o f lights we witness the further attempts to apply the mechanical view. But in the realm o f electric and optical phenomena we meet grave difficulties in this application.

移动电荷作用于磁针。但力不仅取决于距离，还取决于 电荷的速度。 力既不排斥也不吸引，而是 垂直 于连接针和 电荷的线作用。

A moving charge acts upon a magnetic needle. But the force, instead o f depending only upon distance, depends also upon the velocity o f the charge. The force neither repels not attracts but acts perpendicular to the line connecting the needle and the charge.

在光学中，我们必须决定是支持波动论 还是光的粒子论。波在 由粒子组成的介质中传播， 粒子之间有机械力作用 ， 这当然是一个机械概念。但光传播的介质是什么？它的机械特性是什么？在回答这个问题之前，不可能将光学现象归结为机械现象。但解决这个问题的困难是如此之大，以至于我们不得不放弃它，从而也放弃了机械观点。

In optics we have to decide in favour o f the wave theory against the corpuscular theory o f light. Waves spreading in a medium consisting o f particles, with mechanical forces acting between them, are certainly a mechanical concept. But what is the medium through which light spreads and what are its mechanical properties? There is no hope o f reducing the optical phenomena to the mechanical ones before this question is answered. But the difficulties in solving this problem are so great that we have to give it up and thus give up the mechanical views as well.

三、场、相对论

I I I . F I E L D , R E L A T I V I T Y

. 相对论场 ;

F I E L D , R E L A T I V I T Y

场的表象——场 论的两大支柱——场的实在性——场与以太—— 机械支架——以太与运动—— 时间、距离、 相对论——相对论与力学——时空连续体——广义相对论——电梯内外——

The field as representation— The two pillars o f the field theory— The reality o f the field—Field and ether— The mechanical scaffold—Ether and motion— Time, distance, relativity— Relativity and mechanics— The time-space continuum— General relativity— Outside and inside the lift—

几何与实验—广义相对论及其验证—场与物质场 的表示

Geometry and experiment— General relativity and its verification—Field and matter T H E F I E L D A S R E P R E S E N T A T I O N

十九世纪下半叶 ，物理学中出现了新的革命性思想，它们开辟了不同于机械论的新哲学观点。法拉第、麦克斯韦和赫兹的工作成果推动了现代物理学的发展，创造了新的概念，形成了新的现实图景。

D u r i n g the second half o f the nineteenth century new and revolutionary ideas were introduced into physics; they opened the way to a new philosophical view, differing from the mechanical one. The results of the work o f Faraday, Maxwell, and Hertz led to the development o f modern physics, to the creation of new concepts, forming a new picture of reality.

我们现在的任务是描述这些新概念给科学带来的突破，并展示它们如何逐渐变得清晰和强大。我们将尝试逻辑地重建进步的路线，而不太在意时间顺序。

O u r task now is to describe the break brought about in science by these new concepts and to show how they gradually gained clarity and strength. We shall try to reconstruct the line of progress logically, without bothering too much about chronological order.

这些新概念源于电现象，但首次通过力学引入这些概念更为简单。我们知道两个粒子相互吸引，并且这种吸引力随着距离的平方而减小。

The new concepts originated in connection with the phenomena of electricity, but it is simpler to introduce them, for the first time, through mechanics. We know that two particles attract each other and that this force of attraction decreases with the square of the distance.

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我们可以以一种新的方式表示这一事实，尽管很难理解这样做的好处，但我们还是会这样做。我们图中的小圆圈代表一个引力体，比如太阳。实际上，我们的图表应该被想象成一个空间模型，而不是一个平面图。那么，我们的小圆圈代表空间中的一个球体，比如太阳。一个物体，即所谓的测试物体， 被带到太阳附近的某个地方，将沿着连接两个物体中心的线被吸引。因此，我们图中的线条表示测试物体在不同位置的太阳吸引力的方向。每条线上的箭头表示力指向太阳；这意味着力是一种吸引力。这些是 引力场的力线。目前，这只是一个名称，没有理由进一步强调它。我们的绘图有一个特点，稍后会强调。线条

We can represent this fact in a new way, and shall do so even though it is difficult to understand the advantage o f this. The small circle in our drawing represents an attracting body, say, the sun. Actually, our diagram should be imagined as a model in space and not as a drawing on a plane. O ur small circle, then, stands for a sphere in space, say, the sun. A body, the so-called test body, brought somewhere within the vicinity of the sun will be attracted along the line connecting the centres of the two bodies. Thus the lines in our drawing indicate the direction o f the attracting force of the sun for different positions of the test body. The arrow on each line shows that the force is directed toward the sun; this means the force is an attraction. These are the lines o f force o f the gravitational field. For the moment, this is merely a name and there is no reason for stressing it further. There is one characteristic feature of our drawing which will be emphasized later. The lines

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力量的构造是1

o f force are constructed in 1

空间中，无论物质

space, where no matter is

目前，所有的力线，或者简单地说，场，都只表明当一个测试物体被带入构建该场的球体附近时，它将如何表现。

present. For the moment, all the lines o f force, or briefly speaking, the field, indicate only how a test body would behave if brought into the vicinity of the sphere for which the field is constructed.

我们的空间模型中的线总是垂直于球体表面。由于它们从一个点发散，它们在球体附近很密集，而离球体越远，它们就越稀疏。如果我们将与球体的距离增加两倍或三倍，那么在我们的空间模型中，尽管在图中没有，线的密度将减少四到九倍。因此，这些线有双重用途。一方面，它们显示了作用在球体（太阳）附近的物体上的力的方向。另一方面，空间中力线的密度显示了力如何随距离而变化。正确解释的场图表示引力的方向及其对距离的依赖性。人们可以从这样的图中读出引力定律，就像从用文字或精确而经济的数学语言对作用的描述中一样。这种 场表示（我们将称之为场表示）可能看起来清晰有趣，但没有理由相信它标志着任何真正的进步。在引力的情况下，要证明它的实用性将非常困难。有些人可能发现，将这些线视为不仅仅是图画的东西，并想象力穿过它们的真实作用是有帮助的。这可以做到，但随后

The lines in our space model are always perpendicular to the surface of the sphere. Since they diverge from one point, they are dense near the sphere and become less and less so farther away. I f we increase the distance from the sphere twice or three times, then the density of the lines, in our space model, though not in the drawing, will be four or nine times less. Thus the lines serve a double purpose. O n the one hand, they show the direction of the force acting on a body brought into the neighbourhood of the sphere-sun. O n the other hand, the density o f the lines of force in space shows how the force varies with the distance. The drawing of the field, correctly interpreted, represents the direction o f the gravitational force and its dependence on distance. O ne can read the law of gravitation from such a drawing just as well as from a description o f the action in words, or in the precise and economical language o f mathematics. This field representation, as we shall call it, may appear clear and interesting, but there is no reason to believe that it marks any real advance. It would be quite difficult to prove its usefulness in the case o f gravitation. Some may, perhaps, find it helpful to regard these lines as something more than drawings, and to imagine the real actions o f force passing through them. This may be done, but then the

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力的作用速度必须被假定为无穷大！根据牛顿定律，两个物体之间的力只取决于距离；时间不受影响。力必须在短时间内从一个物体传递到另一个物体！但是，由于无限速度的运动对任何理性的人来说都没有什么意义，因此试图使我们的绘图不仅仅是一个模型是徒劳的。

speed o f the actions along the lines of force must be assumed as infinitely great! The force between two bodies, according to Newton’s law, depends only on distance; time does not enter the picture. The force has to pass from one body to another in no tim e ! But, as motion with infinite speed cannot mean much to any reasonable person, an attempt to make our drawing something more than a model leads nowhere.

不过，我们现在并不打算讨论引力问题，它仅作为一个介绍，简化对电学理论中类似推理方法的解释。

We do not intend, however, to discuss the gravitational problem just now It served only as an introduction, simplifying the explanation o f similar methods of reasoning in the theory o f electricity.

我们首先要讨论一下给我们的力学解释带来严重困难的实验。电流流过一个圆形的导线电路。电路中间有一根磁针。电流开始流动的那一刻，出现了一种新的力，作用在磁极上，垂直于连接导线和磁极的任何一条线。如果这种力是由循环电荷引起的，那么根据罗兰德的实验，它取决于电荷的速度。这些实验事实与哲学观点相矛盾，哲学观点认为所有力都必须作用在连接粒子的线上，并且只能取决于距离。

We shall begin with a discussion o f the experiment which created serious difficulties in our mechanical interpretation. We had a current flowing through a wire circuit in the form of a circle. In the middle of the circuit was a magnetic needle. The moment the current began to flow a new force appeared, acting on the magnetic pole, and perpendicular to any line connecting the wire and the pole. This force, if caused by a circulating charge, depended, as shown by Row land’s experiment, on the velocity of the charge. These experimental facts contradicted the philosophical view that all forces must act on the line connecting the particles and can depend only upon distance.

电流作用于磁极的力的确切表达式相当复杂，甚至比重力的表达式复杂得多。然而，我们可以尝试将这种作用形象化，就像我们在重力的情况下所做的那样。

The exact expression for the force of a current acting on a magnetic pole is quite complicated, much more so, indeed, than the expression for gravitational forces. We can, however, attempt to visualize the actions just as we did in the case o f a gravitational force.

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我们的问题是：电流对位于其附近的磁极作用的力是什么？用语言描述这种力相当困难。甚至数学公式也会很复杂和笨拙。最好用一幅图来表示我们所知道的所有作用力，或者更确切地说，用一个带有力线的空间模型来表示。一个磁极只与另一个磁极相连而形成偶极子，这造成了一些困难。然而，我们总是可以想象磁针的长度，使得只需要考虑作用在靠近电流的极点上的力。另一个极点离得足够远，作用在它上面的力可以忽略不计。为了避免歧义，我们应当说靠近导线的磁极是正极。

O ur question is: with what force does the current act upon a magnetic pole placed somewhere in its vicinity? It would be rather difficult to describe this force in words. Even a mathematical formula would be complicated and awkward. It is best to represent all we know about the acting forces by a drawing, or rather by a spatial model, with lines of force. Some difficulty is caused by the fact that a magnetic pole exists only in connection with another magnetic pole, forming a dipole. We can, however, always imagine the magnetic needle of such length that only the force acting upon the pole nearer the current has to be taken into account. The other pole is far enough away for the force acting upon it to be negligible. T o avoid ambiguity we shall say that the magnetic pole brought nearer to the wire is the positive one.

从我们的图中可以读出作用于正磁极的力的特性。

The character of the force acting upon the positive magnetic pole can be read from our drawing.

首先，我们注意到电线附近有一个箭头，指示电流的方向，从高到低

First we notice an arrow near the wire indicating the direction of the current, from higher to lower

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势能。所有其他线只是属于该电流并位于某个平面上的力线。如果画得正确，它们会告诉我们力矢量的方向，该力矢量表示电流对给定正磁极的作用，以及该矢量的长度。众所周知，力是一个矢量，要确定它，我们必须知道它的方向和长度。我们主要关心作用在极上的力的方向问题。

potential. A ll other lines are just lines o f force belonging to this current and lying on a certain plane. I f drawn properly, they tell us the direction of the force vector representing the action o f the current on a given positive magnetic pole as well as something about the length of this vector. Force, as we know, is a vector, and to determine it we must know its direction as well as its length. We are chiefly concerned with the problem of the direction o f the force acting upon a pole.

我们的问题是：我们如何从图中找到空间中任意一点的力的方向？

O u r question is: how can we find, from the drawing, the direction o f the force, at any point in space?

从这种模型中读取力的方向的规则并不像我们之前的例子那样简单，因为力线是直线。在我们的下一个图中，为了阐明这一过程，只画了一条力线。力矢量位于力线的切线上，如图所示。力矢量的箭头和力线上的箭头指向同一方向。因此，这是力作用于磁极的方向

The rule for reading the direction o f a force from such a model is not as simple as in our previous example, where the lines o f force were straight. In our next diagram only one line of force is drawn in order to clarify the procedure. The force vector lies on the tangent to the line of force, as indicated. The arrow of the force vector and the arrows on the line of force point in the same direction. Thus this is the direction in which the force acts on a magnetic pole at this

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点。一幅好的图画，或者说一个好的模型，也能告诉我们任何一点力矢量的长度。线更密集的地方，也就是靠近导线的地方，力矢量应该更长；线不那么密集的地方，也就是远离导线的地方，力矢量应该更短。

point. A good drawing, or rather a good model, also tells us something about the length of the force vector at any point. This vector has to be longer where the lines are denser, i.e., near the wire, shorter where the lines are less dense, i.e., far from the wire.

这样，力线，或者说场，使我们能够确定空间中任何一点磁极受到的力。目前，这是我们精心构建场的唯一理由。了解了场所表达的内容后，我们将以更深入的兴趣研究与电流相对应的力线。这些线是围绕导线的圆圈，位于与导线所在平面垂直的平面上。

In this way, the lines of force, or in other words, the field, enable us to determine the forces acting on a magnetic pole at any point in space. This, for the time being, is the only justification for our elaborate construction of the field. Knowing what the field expresses, we shall examine with a far deeper interest the lines o f force corresponding to the current. These lines are circles surrounding the wire and lying on the plane perpendicular to that in which the wire is situated.

从图中读出力的特性，我们再次得出结论：力作用的方向垂直于连接导线和磁极的任何线，因为圆的切线总是垂直于其半径。我们对作用力的全部知识可以总结为场的构造。我们将场的概念夹在电流和磁极的概念之间，以便以简单的方式表示作用力。

Reading the character of the force from the drawing, we come once more to the conclusion that the force acts in a direction perpendicular to any line connecting the wire and the pole, for the tangent to a circle is always perpendicular to its radius. O ur entire knowledge of the acting forces can be summarized in the construction of the field. We sandwich the concept of the field between that of the current and that of the magnetic pole in order to represent the acting forces in a simple way.

任何电流都与磁场有关，也就是说，力总是作用在靠近电流流过的导线的磁极上。顺便说一下，这一特性使我们能够构造灵敏的仪器来检测电流的存在。一旦学会了如何读取特征，

Every current is associated with a magnetic field, i.e., a force always acts on a magnetic pole brought near the wire through which a current flows. We may remark in passing that this property enables us to construct sensitive apparatus for detecting the existence of a current. Once having learned how to read the charac-

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除了来自电流场模型的磁力之外，我们将始终画出电流流过的导线周围的场，以表示空间中任意一点的磁力作用。我们的第一个例子是所谓的螺线管。事实上，它是如图所示的线圈。我们的目标是通过实验尽可能地了解与流过螺线管的电流相关的磁场，并将这些知识融入场的构建中。附图显示了我们的结果。弯曲的力线是闭合的，并以电流磁场特有的方式围绕螺线管。

ter of the magnetic forces from the field model o f a current, we shall always draw the field surrounding the wire through which the current flows, in order to represent the action o f the magnetic forces at any point in space. O ur first example is the so-called solenoid. This is, in fact, a coil of wire as shown in the drawing. O ur aim is to learn, by experiment, all we can about the magnetic field associated with the current flowing through a solenoid and to incorporate this knowledge in the construction o f a field. A drawing represents our result. The curved lines of force are closed, and surround the solenoid in a way characteristic of the magnetic field of a current.

条形磁铁的磁场可以用与电流相同的方式表示。另一幅图显示了这一点。力线从正极指向负极。力矢量总是位于力线的切线上，并且在极点附近最长，因为这些点处的线密度最大。力矢量表示

The field of a bar magnet can be represented in the same way as that of a current. Another drawing shows this. The lines of force are directed from the positive to the negative pole. The force vector always lies on the tangent to the line of force and is longest near the poles because the density of the lines is greatest at these points. The force vector represents the action of the

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磁铁位于正磁极上。在这种情况下，磁场的“来源”是磁铁，而不是电流。

magnet on a positive magnetic pole. In this case the magnet and not the current is the “ source” o f the field.

我们应该仔细比较最后两幅画。

O ur last two drawings should be carefully compared.

第一种情况是电流流过螺线管的磁场；第二种情况是条形磁铁的磁场。我们忽略螺线管和条形磁铁，只观察两个外部磁场。我们立即注意到它们的特性完全相同；在每种情况下，力线都从螺线管或条形磁铁的一端引向另一端。

In the first, we have the magnetic field of a current flowing through a solenoid; in the second, the field o f a bar magnet. Let us ignore both the solenoid and the bar and observe only the two outside fields. We immediately notice that they are of exactly the same character; in each case the lines of force lead from one end of the solenoid or bar to the other.

场的表述产生了它的第一个结果！如果我们的场的构造没有揭示这一点，那么很难看出流经螺线管的电流和条形磁铁之间的任何强烈相似性。

The field representation yields its first fru it! It would be rather difficult to see any strong similarity between the current flowing through a solenoid and a bar magnet if this were not revealed by our construction o f the field.

现在，场的概念可以接受更为严格的检验。我们很快就会看到，它是否只是作用力的一种新表示。我们可以推理：假设场以独特的方式表征由其来源决定的所有作用。这只是一个猜测。这意味着，如果螺线管和条形磁铁具有相同的

The concept o f field can now be put to a much more severe test. We shall soon see whether it is anything more than a new representation of the acting forces. We could reason: assume, for a moment, that the field characterizes all actions determined by its sources in a unique way. This is only a guess. It would mean that if a solenoid and a bar magnet have the same

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领域，那么它们的所有影响也必须是相同的。

field, then all their influences must also be the same.

这意味着两个带电螺线管的行为就像两根条形磁铁，它们相互吸引或排斥，就像条形磁铁的情况一样，取决于它们的相对位置。这也意味着螺线管和条形磁铁相互吸引或排斥的方式与两根条形磁铁相同。简而言之，这意味着有电流流过的螺线管和相应的条形磁铁的所有动作都是相同的，因为只有磁场才能控制它们，而且这两种情况下的磁场具有相同的特性。实验完全证实了我们的猜测！

It would mean that two solenoids, carrying electric currents, behave like two bar magnets, that they attract or repel each other, depending exactly as in the case of bars, on their relative positions. It would also mean that a solenoid and a bar attract or repel each other in the same way as two bars. Briefly speaking, it would mean that all actions o f a solenoid through which a current flows and of a corresponding bar magnet are the same, since the field alone is responsible for them, and the field in both cases is of the same character. Experiment fully confirms our guess !

如果没有场的概念，要找到这些事实将是多么困难！作用在有电流通过的导线和磁极之间的力的表达式非常复杂。在两个螺线管的情况下，我们必须研究两个电流相互作用的力。但如果我们这样做，借助场，当看到螺线管的场和条形磁铁的场之间的相似性时，我们就会立即注意到所有这些作用的特征。

How difficult it would be to find those facts without the concept o f field! The expression for a force acting between a wire through which a current flows and a magnetic pole is very complicated. In the case o f two solenoids, we should have to investigate the forces with which two currents act upon each other. But if we do this, with the help o f the field, we immediately notice the character o f all those actions at the moment when the similarity between the field o f a solenoid and that of a bar magnet is seen.

我们有权将场视为比我们最初认为的更多的东西。场的性质本身似乎对现象的描述至关重要；来源的差异并不重要。

We have the right to regard the field as something much more than we did at first. The properties of the field alone appear to be essential for the description of phenomena; the differences in source do not matter.

场的概念通过引出新的实验事实而显示出其重要性。

The concept of field reveals its importance by leading to new experimental facts.

事实证明，场是一个非常有用的概念。它最初是放置在源和磁场之间的某种东西。

The field proved a very helpful concept. It began as something placed between the source and the magnetic

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针为了描述1

needle in order to describ 1

是作用力。

e the acting force. It was

被认为是电流的“代理”，电流的所有动作都是通过它进行的。但现在代理也充当了解释者的角色，将定律翻译成简单、清晰、易于理解的语言。

thought o f as an “ agent’ ’ of the current, through which all action of the current was performed. But now the agent also acts as an interpreter, one who translates the laws into a simple, clear language, easily understood.

场描述的首次成功表明，间接地考虑电流、磁体和电荷的所有作用可能很方便，即借助场作为解释器。场可以被视为始终与电流相关的事物。

The first success of the field description suggests that it may be convenient to consider all actions of currents, magnets and charges indirectly, i.e., with the help of the field as an interpreter. A field may be regarded as something always associated with a current.

即使没有磁极来验证它的存在，它仍然在那里。让我们试着持续追踪这个新线索。

It is there even in the absence of a magnetic pole to test its existence. Let us try to follow this new clue consistently.

带电导体的场可以以与引力场、电流场或磁体场大致相同的方式引入。这又是一个最简单的例子！要设计带正电球体的场，我们必须问什么样的力作用在球体上

The field o f a charged conductor can be introduced in much the same way as the gravitational field, or the field of a current or magnet. Again only the simplest exam ple! T o design the field of a positively charged sphere, we must ask what kind of forces are acting on

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将一个小的带正电的测试体放在场源（带电球）附近。我们使用带正电而不是带负电的测试体，这只是一个惯例，表示力线上的箭头应该朝哪个方向画。

a small positively charged test body brought near the source of the field, the charged sphere. The fact that we use a positively and not a negatively charged test body is merely a convention, indicating in which direction the arrows on the line of force should be drawn.

由于库仑定律与牛顿定律相似，该模型与引力场模型（第 130 页）类似。两个模型之间的唯一区别是箭头指向相反的方向。

The model is analogous to that of a gravitational field (p. 130) because of the similarity between Coulom b’s law and Newton’s. The only difference between the two models is that the arrows point in opposite directions.

确实，我们有两个正电荷之间的排斥力和两个质量之间的吸引力。然而，带负电荷的球体的场将与引力场相同，因为小的正测试电荷将被引力源吸引。如果电极和磁极都处于静止状态，它们之间就不会发生作用，既没有吸引力也没有排斥力。用场语言表达同样的事实，

Indeed, we have repulsion of two positive charges and attraction of two masses. However, the field of a sphere with a negative charge will be identical with a gravitational field since the small positive testing charge will be attracted by the source o f the I f both electric and magnetic poles are at rest, there is no action between them, neither attraction nor repulsion. Expressing the same fact in the field language,

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我们可以说：静电场不会影响静磁场，反之亦然。“静场”是指不随时间变化的场。

we can say: an electrostatic field does not influence a magnetostatic one and vice versa. The words “ static field” mean a field that does not change with time.

如果没有外力干扰，磁铁和电荷将永远彼此靠近。

The magnets and charges would rest near one another for an eternity if no external forces disturbed them.

静电场、静磁场和引力场都具有不同的特性。它们不会混合；各自保留着自己的个性，不受其他场的影响。

Electrostatic, magnetostatic and gravitational fields are all o f different character. They do not m ix; each preserves its individuality regardless o f the others.

让我们回到迄今为止处于静止状态的电球，并假设它由于某种外力的作用而开始移动。带电球移动。在场语言中，这句话是：电荷场随时间变化。但是，正如我们从罗兰德的实验中已经知道的那样，这个带电球的运动相当于电流。

Let us return to the electric sphere which was, until now, at rest, and assume that it begins to move owing to the action of some external force. The charged sphere moves. In the field language this sentence reads: the field of the electric charge changes with time. But the motion o f this charged sphere is, as we already know from Row land’s experiment, equivalent to a current.

此外，每个电流都伴随着磁场。因此，我们的论证链条是：电荷运动电场变化电流伴随磁场。

Further, every current is accompanied by a magnetic field. Thus the chain of our argument is: motion o f charge change of an electric field current associated magnetic field.

因此，我们得出结论： 电荷运动产生的电场的变化总是伴随着 磁场的变化。

We, therefore, conclude: The change o f an electric field produced by the motion o f a charge is always accompanied by a magnetic field.

我们的结论是基于奥斯特的实验，但涵盖的内容远不止这些。它包含这样的认识：随时间变化的电场与磁场的关联对于我们进一步的论证至关重要。

O ur conclusion is based on Oersted’s experiment, but it covers much more. It contains the recognition that the association o f an electric field, changing in time, with a magnetic field is essential for our further argument.

只要电荷处于静止状态，就只有一个电

As long as a charge is at rest there is only an electro-

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静场。但是一旦电荷开始移动，就会出现磁场。我们可以说得更多。如果电荷更大并且移动得更快，电荷运动产生的磁场就会更强。

static field. But a magnetic field appears as soon as the charge begins to move. We can say more. The magnetic field created by the motion o f the charge will be stronger if the charge is greater and if it moves faster.

这也是罗兰实验的结果。

This also is a consequence o f Rowland’s experiment.

再次使用场语言，我们可以说：电场变化得越快，伴随的磁场就越强。

Once again using the field language, we can say: the faster the electric field changes, the stronger the accompanying magnetic field.

我们在此尝试将根据旧的机械观点构建的流体语言中的熟悉事实翻译成新的场语言。

We have tried here to translate familiar facts from the language o f fluids, constructed according to the old mechanical view, into the new language o f fields.

我们稍后会看到我们的新语言是多么清晰、具有指导意义和影响深远。

We shall see later how clear, instructive, and far-reaching our new language is.

双支柱软理论

T H E T W O P I L L A R S O F T H E F I E L D T H E O R Y

“ 电场的变化伴随着磁场的变化。” 如果我们互换“ 磁 ” 和“ 电 ” 这两个词，我们的句子就是：“ 磁场的变化伴随着电场的变化。”

“ The change of an electric field is accompanied by a magnetic field.” I f we interchange the words “ magnetic” and “ electric” , our sentence reads: “ The change of a magnetic field is accompanied by an electric field.”

只有实验才能决定这个说法是否正确。但是，提出这个问题的想法是通过使用领域语言来提出的。

O nly an experiment can decide whether or not this statement is true. But the idea o f formulating this problem is suggested by the use o f the field language.

就在一百多年前，法拉第做了一个实验，导致了感应电流的伟大发现。

Ju st over a hundred years ago, Faraday performed an experiment which led to the great discovery of induced currents.

演示非常简单。我们只需要一个螺线管或其他电路、一个条形磁铁，以及用于检测电流存在的多种类型的设备之一。首先，将条形磁铁静止在螺线管附近，形成一个封闭的

The demonstration is very simple. We need only a solenoid or some other circuit, a bar magnet, and one o f the many types of apparatus for detecting the existence o f an electric current. T o begin with, a bar magnet is kept at rest near a solenoid which forms a closed

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电路。由于没有电源，所以导线中没有电流流过。只有条形磁铁的静磁场，该磁场不随时间变化。

circuit. No current flows through the wire, for no source is present. There is only the magnetostatic field of the bar magnet which does not change with time.

现在，我们可以快速改变磁铁的位置，要么把它移走，要么把它移近螺线管，随你喜欢。此时，电流会出现很短的时间，然后消失。

Now, we quickly change the position o f the magnet either by removing it or by bringing it nearer the solenoid, whichever we prefer. A t this moment, a current will appear for a very short time and then vanish.

每当磁铁的位置改变时，电流就会重新出现，并且可以通过足够灵敏的仪器检测到。但是从场论的角度来看，电流意味着存在一个电场，迫使电流体流过导线。当磁铁再次静止时，电流和电场也会消失。

Whenever the position o f the magnet is changed, the current reappears, and can be detected by a sufficiently sensitive apparatus. But a current— from the point of view of the field theory— means the existence of an electric field forcing the flow o f the electric fluids through the wire. The current, and therefore the electric field, too, vanishes when the magnet is again at rest.

想象一下，场语言是未知的，并且必须用旧机械概念的语言定性和定量地描述这个实验的结果。我们的实验表明：通过磁偶极子的运动产生了一种新的力，使导线中的电流体移动。

Imagine for a moment that the field language is unknown and the results of this experiment have to be described, qualitatively and quantitatively, in the language of old mechanical concepts. O u r experiment then shows: by the motion o f a magnetic dipole a new force was created, moving the electric fluid in the wire.

下一个问题是：这种力量取决于什么？这个问题很难回答。

The next question would be: upon what does this force depend? This would be very difficult to answer.

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我们应该研究磁力与磁体速度、形状和电路形状之间的关系。此外，如果用旧语言来解释，这个实验根本无法告诉我们感应电流是否可以通过另一个载流电路的运动而不是条形磁铁的运动来激发。

We should have to investigate the dependence o f the force upon the velocity of the magnet, upon its shape, and upon the shape o f the circuit. Furthermore, this experiment, if interpreted in the old language, gives us no hint at all as to whether an induced current can be excited by the motion o f another circuit carrying a current, instead o f by motion of a bar magnet.

如果我们使用场的语言，并再次相信我们的原理，即动作由场决定，那么情况就完全不同了。我们立刻就会发现，电流流过的螺线管的作用与条形磁铁一样好。图中显示了两个螺线管：一个小螺线管，电流流过；另一个大螺线管，在其中检测到感应电流。我们可以移动小螺线管，就像我们之前移动条形磁铁一样，在大螺线管中产生感应电流。此外，我们可以通过产生和消除电流（即打开和关闭电路）来产生和消除磁场，而不是移动小螺线管。再一次，场论提出的新事实得到了实验的证实！

It is quite a different matter if we use the field language and again trust our principle that the action is determined by the field. We see at once that a solenoid through which a current flows would serve as well as a bar magnet. The drawing shows two solenoids: one, small, through which a current flows, and the other, in which the induced current is detected, larger. We could move the small solenoid, as we previously moved the bar magnet, creating an induced current in the larger solenoid. Furthermore, instead of moving the small solenoid, we could create and destroy a magnetic field by creating and destroying the current, that is, by opening and closing the circuit. Once again, new facts suggested by the field theory are confirmed by experim ent!

让我们举一个更简单的例子。我们有一根闭合的电线

Let us take a simpler example. We have a closed wire

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没有任何 c 1 来源

without any source of c 1

当前。在某个地方

urrent. Somewhere in the

附近是一个磁场。无论这个磁场的来源是另一个有电流流过的电路还是条形磁铁，对我们来说都没有任何意义。我们的图显示了闭合电路和磁力线。用场语言来描述感应现象的定性和定量描述非常简单。如图所示，一些力线穿过导线所包围的表面。我们必须考虑力线切割以导线为边缘的平面的那部分。只要场不发生变化，就不会存在电流，无论其强度有多大。

vicinity is a magnetic field. It means nothing to us whether the source of this magnetic field is another circuit through which an electric current flows, or a bar magnet. O ur drawing shows the closed circuit and the magnetic lines of force. The qualitative and quantitative description of the induction phenomena is very simple in terms of the field language. As marked on the drawing, some lines of force go through the surface bounded by the wire. We have to consider the lines of force cutting that part of the plane which has the wire for a rim. No electric current is present so long as the field does not change, no matter how great its strength.

但是，一旦穿过被导线包围的表面的线数发生变化，电流就会开始流过边缘导线。电流由穿过表面的线数的变化决定，不管这种变化是如何引起的。力线数量的这种变化是唯一的基本概念

But a current begins to flow through the rim-wire as soon as the number of lines passing through the surface surrounded by wire changes. The current is determined by the change, however it may be caused, of the number of lines passing the surface. This change in the number of lines of force is the only essential concept

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对于感应电流的定性和定量描述。“线数变化”意味着线密度变化，我们记得，这意味着场强变化。

for both the qualitative and the quantitative descriptions o f the induced current. “ The number o f lines changes ” means that the density o f the lines changes and this, we remember, means that the field strength changes.

这些就是我们推理链中的要点：磁场的变化、感应电流、电荷的运动、电场的存在。

These then are the essential points in our chain of reasoning: change o f magnetic field induced current motion o f charge existence of an electric field.

因此： 变化的磁场会伴随着 电场的出现。

Therefore: a changing magnetic field is accompanied by an electric field.

这样，我们就找到了电场和磁场理论的两个最重要的支撑支柱。第一个是变化的电场和磁场之间的联系。它源于奥斯特对磁针偏转的实验，并得出了这样的结论： 变化的电场 伴随着磁场。

Thus we have found the two most important pillars of support for the theory o f the electric and magnetic field. The first is the connection between the changing electric field and the magnetic field. It arose from Oersted’s experiment on the deflection o f a magnetic needle and led to the conclusion: a changing electric field is accompanied by a magnetic field.

第二种是将变化的磁场与感应电流联系起来，源于法拉第的实验。两者都构成了定量描述的基础。

The second connects the changing magnetic field with the induced current and arose from Faraday’s experiment. Both formed a basis for quantitative description.

再次，伴随磁场变化的电场似乎是真实存在的。我们之前必须想象没有测试极的电流的磁场。同样，我们必须在这里声称，即使导线没有测试感应电流的存在，电场也存在。

Again the electric field accompanying the changing magnetic field appears as something real. We had to imagine, previously, the magnetic field of a current existing without the testing pole. Similarly, we must claim here that the electric field exists without the wire testing the presence o f an induced current.

事实上，我们的双支柱结构可以简化为只有一个，即基于奥斯特实验的结构

In fact, our two-pillar structure could be reduced to only one, namely, to that based on Oersted’s experi-

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法拉第实验的结果可由此根据能量守恒定律推导出来。我们采用双柱结构只是为了清晰和经济。

ment. The result of Faraday’s experiment could be deduced from this with the law o f conservation of energy. We used the two-pillared structure only for the sake o f clearness and economy.

还应该提到场描述的另一个结果。有一个电路，电流通过该电路，例如，电流源是伏打电池。导线和电流源之间的连接突然断开。当然，现在没有电流了！但在这个短暂的中断期间，发生了一个复杂的过程，这个过程也可以被场论预见到。在电流中断之前，导线周围有一个磁场。电流中断后，磁场就不复存在了。因此，电流中断后，磁场就消失了。穿过导线所包围表面的力线数量变化非常快。但这种快速变化，不管它是如何产生的，都必然会产生感应电流。真正重要的是，如果变化越大，磁场的变化就越大，感应电流就越强。这个结果是对理论的另一个检验。

O ne more consequence o f the field description should be mentioned. There is a circuit through which a current flows, with, for instance, a voltaic battery as the source of the current. The connection between the wire and the source o f the current is suddenly broken. There is, o f course, no current n ow ! But during this short interruption an intricate process takes place, a process which could again have been foreseen by the field theory. Before the interruption o f the current, there was a magnetic field surrounding the wire. This ceased to exist the moment the current was interrupted. Therefore, through the interruption o f a current, a magnetic field disappeared. The number o f lines of force passing through the surface surrounded by the wire changed very rapidly. But such a rapid change, however it is produced, must create an induced current. W hat really matters is the change of the magnetic field making the induced current stronger if the change is greater. This consequence is another test for the theory.

电流的断开必定伴随着强烈的瞬时感应电流的出现。实验再次证实了这一预测。

The disconnection of a current must be accompanied by the appearance of a strong, momentary induced current. Experiment again confirms the prediction.

任何曾经切断过电流的人都一定注意到了火花的出现。这种火花揭示了磁场快速变化引起的强大电位差。

Anyone who has ever disconnected a current must have noticed that a spark appears. This spark reveals the strong potential differences caused by the rapid change of the magnetic field.

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可以从另一个角度来看待同一个过程，即能量角度。磁场消失了，火花产生了。火花代表能量，因此磁场也必须如此。为了一致地使用场的概念及其语言，我们必须将磁场视为能量的储存。

T he same process can be looked at from a different point of view, that of energy. A magnetic field disappeared and a spark was created. A spark represents energy, therefore so also must the magnetic field. T o use the field concept and its language consistently, we must regard the magnetic field as a store of energy.

只有这样，我们才能按照能量守恒定律来描述电磁现象。

O n ly in this way shall we be able to describe the electric and magnetic phenomena in accordance with the law o f conservation of energy.

场最初是一个有用的模型，后来变得越来越真实。它帮助我们理解旧的事实，并引导我们找到新的事实。将能量归因于场是发展中的又一步，在这一发展中，场的概念越来越受到重视，而对机械观点至关重要的物质概念则越来越受到压制。

Starting as a helpful model, the field became more and more real. It helped us to understand old facts and led us to new ones. The attribution of energy to the field is one step farther in the development in which the field concept was stressed more and more, and the concepts of substances, so essential to the mechanical point o f view, were more and more suppressed.

现实情况

T H E R E A L I T Y O F T H E F I E L D

场的定律的定量数学描述总结在所谓的麦克斯韦方程中。迄今为止提到的事实导致了这些方程的形成，但它们的内容比我们能够指出的要丰富得多。它们的简单形式隐藏着只有经过仔细研究才能揭示的深度。

T he quantitative, mathematical description o f the laws o f the field is summed up in what are called M axw ell’s equations. The facts mentioned so far led to the formulation o f these equations, but their content is much richer than we have been able to indicate. Their simple form conceals a depth revealed only by careful study.

这些方程的建立是牛顿以来物理学中最重要的事件，不仅因为它们内容丰富，还因为它们形成了一种新型定律的模式。

T he formulation of these equations is the most important event in physics since Newton’s time, not only because of their wealth of content, but also because they form a pattern for a new type of law.

麦克斯韦方程组的特征出现在现代物理学的所有其他方程中，

T he characteristic features o f M axw ell’s equations, appearing in all other equations o f modem physics, arc

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一句话概括，麦克斯韦方程组就是代表场的结构的定律。

summarized in one sentence. Maxwell’s equations are laws representing the structure of the field.

为什么麦克斯韦方程的形式和性质与经典力学方程不同？

Why do Maxwell’s equations differ in form and character from the equations o f classical mechanics?

这些方程描述场的结构意味着什么？我们怎么可能从奥斯特和法拉第的实验结果中得出一种新的定律，而这种定律对物理学的进一步发展如此重要？

What does it mean that these equations describe the structure of the field? How is it possible that, from the results of Oersted’s and Faraday’s experiments, we can form a new type of law, which proves so important for the further development of physics?

我们已经从奥斯特的实验中看到了磁场如何缠绕在变化的电场上。我们也从法拉第的实验中看到了电场如何缠绕在变化的磁场上。为了概述麦克斯韦理论的一些特征，让我们暂时把注意力集中在其中一个实验上，比如法拉第的实验。我们再画一张图，其中电流是由变化的磁场感应出来的。我们已经知道，感应电流

We have already seen, from Oersted’s experiment, how a magnetic field coils itself around a changing electric field. We have seen, from Faraday’s experiment, how an electric field coils itself around a changing magnetic field. T o outline some o f the characteristic features of M axwell’s theory, let us, for the moment, focus all our attention on one of these experiments, say, on that of Faraday. We repeat the drawing in which an electric current is induced by a changing magnetic field. We already know that an induced current

如果出现 0 的数量

appears if the number of 0

穿过导线所围表面的磁力线会发生变化。如果磁场发生变化或电路变形或移动，则会出现电流：如果穿过表面的磁力线数量发生变化，则无论这种变化是如何引起的。考虑所有这些不同的可能性并讨论它们的具体影响，必然会导致一个非常复杂的理论。但是，我们能不能简化我们的问题？让我们试着从我们的考虑中消除所有与电路形状、电路长度、导线所围表面相关的内容。让我们想象一下，我们最后一张图中的电路变得越来越小，逐渐缩小到一个非常小的电路，包围着空间中的某个点。那么，与形状和大小相关的一切都无关紧要。在这个封闭曲线缩小到一个点的极限过程中，大小和形状会自动从我们的考虑中消失，我们得到了在任意时刻在空间中任意一点连接磁场和电场变化的定律。

lines of force, passing the surface bounded by the wire, changes. Then the current will appear if the magnetic field changes or the circuit is deformed or m oved: if the number o f magnetic lines passing through the surface is changed, no matter how this change is caused. T o take into account all these various possibilities, to discuss their particular influences, would necessarily lead to a very complicated theory. But can we not simplify our problem? Let us try to eliminate from our considerations everything which refers to the shape o f the circuit, to its length, to the surface enclosed by the wire. Let us imagine that the circuit in our last drawing becomes smaller and smaller, shrinking gradually to a very small circuit enclosing a certain point in space. Then everything concerning shape and size is quite irrelevant. In this limiting process where the closed curve shrinks to a point, size and shape automatically vanish from our considerations and we obtain laws connecting changes o f magnetic and electric field at an arbitrary point in space at an arbitrary instant.

因此，这是迈向麦克斯韦方程组的主要步骤之一。这又是一个在想象中重复法拉第实验的理想化实验，电路缩小到一个点。

Thus, this is one of the principal steps leading to Maxwell’s equations. It is again an idealized experiment performed in imagination by repeating Faraday’s experiment with a circuit shrinking to a point.

我们其实应该称它为半步而不是整步。到目前为止，我们的注意力都集中在法拉第的实验上。但基于奥斯特实验的场论的另一个支柱也必须同样仔细地以类似的方式考虑。在这方面

We should really call it half a step rather than a whole one. So far our attention has been focused on Faraday’s experiment. But the other pillar o f the field theory, based on Oersted’s experiment, must be considered just as carefully and in a similar manner. In this

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实验磁性 1

experiment the magnetic 1

力线本身卷绕

lines of force coil themselves

电流周围的圆形磁力线收缩到一点，进行第二个半步，整个步骤得到空间任意一点、任意时刻磁场与电场变化的联系。

around the current. By shrinking the circular magnetic lines of force to a point, the second half-step is performed and the whole step yields a connection between the changes of the magnetic and electric fields at an arbitrary point in space and at an arbitrary instant.

但还有一个必不可少的步骤。根据法拉第的实验，必须有一根导线来测试电场的存在，就像在奥斯特的实验中必须有一个磁极或针来测试磁场的存在一样。但麦克斯韦的新理论思想超越了这些实验事实。在麦克斯韦的理论中，电场和磁场，或者简而言之，电磁场，是真实存在的。电场是由变化的磁场完全独立地产生的，无论是否有导线来测试它的存在；磁场是由变化的电场产生的，无论是否有磁极来测试它的存在。

But still another essential step is necessary. According to Faraday’s experiment, there must be a wire testing the existence o f the electric field, just as there must be a magnetic pole, or needle, testing the existence o f a magnetic field in Oersted’s experiment. But Maxwell’s new theoretical idea goes beyond these experimental facts. The electric and magnetic field or, in short, the electromagnetic field is, in Maxwell’s theory, something real. The electric field is produced by a changing magnetic field, quite independently, whether or not there is a wire to test its existence; a magnetic field is produced by a changing electric field, whether or not there is a magnetic pole to test its existence.

因此，两个基本步骤导致了麦克斯韦方程的出现。

Thus two essential steps led to Maxwell’s equations.

第一步：在考虑奥斯特和罗兰德的实验时，环绕电流和变化的电场的磁场的圆线必须收缩到一个点；在考虑法拉第的实验时，环绕变化的磁场的电场的圆线必须收缩到一个点。第二步是将场视为真实的东西；电磁场一旦产生，就会根据麦克斯韦定律存在、作用和变化。

The first: in considering Oersted’s and Row land’s experiments, the circular line o f the magnetic field coiling itself around the current and the changing electric field had to be shrunk to a point; in considering Faraday’s experiment, the circular line o f the electric field coiling itself around the changing magnetic field had to be shrunk to a point. The second step consists of the realization of the field as something real; the electromagnetic field once created exists, acts, and changes according to M axwell’s laws.

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麦克斯韦方程组描述了电磁场的结构。整个空间都是这些定律的场景，而不像机械定律那样，只有存在物质或电荷的点。

Maxwell’s equations describe the structure o f the electromagnetic field. A ll space is the scene of these laws and not, as for mechanical laws, only points in which matter or charges are present.

我们还记得力学中的情况。通过了解粒子在某一瞬间的位置和速度，了解作用力，就可以预见粒子的整个未来路径。在麦克斯韦理论中，如果我们只知道某一瞬间的场，我们就可以从理论方程中推断出整个场在空间和时间中将如何变化。麦克斯韦方程使我们能够追踪场的历史，就像力学方程使我们能够追踪物质粒子的历史一样。

We remember how it was in mechanics. By knowing the position and velocity o f a particle at one single instant, by knowing the acting forces, the whole future path o f the particle could be foreseen. In M axw ell’s theory, if we know the field at one instant only, we can deduce from the equations o f the theory how the whole field will change in space and time. M axw ell’s equations enable us to follow the history of the field, just as the mechanical equations enabled us to follow the history of material particles.

但力学定律和麦克斯韦定律之间仍然存在一个本质区别。比较牛顿引力定律和麦克斯韦场定律，可以突出这些方程所表达的一些特征。

But there is still one essential difference between mechanical laws and M axw ell’s laws. A comparison o f Newton’s gravitational laws and M axw ell’s field laws will emphasize some of the characteristic features expressed by these equations.

借助牛顿定律，我们可以从太阳和地球之间的作用力推导出地球的运动。这些定律将地球的运动与遥远的太阳的作用联系起来。地球和太阳虽然相距甚远，但都是力的作用的参与者。

With the help of Newton’s laws we can deduce the motion of the earth from the force acting between the sun and the earth. The laws connect the motion o f the earth with the action of the far-off sun. The earth and the sun, though so far apart, are both actors in the play o f forces.

在麦克斯韦的理论中，不存在任何物质行为者。

In M axw ell’s theory there are no material actors.

这个理论的数学方程表达了电磁场的规律。它们不像牛顿定律那样，把两个相隔很远的事件联系起来；它们没有把这里发生的事情与

The mathematical equations of this theory express the laws governing the electromagnetic field. They do not, as in Newton’s laws, connect two widely separated events; they do not connect the happenings here with

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那里的条件。此时此刻 的场取决于 刚刚过去 某一时刻的场。如果我们知道此时此刻发生的事情，这些方程可以让我们预测空间中稍远一点和时间稍晚一点会发生什么。它们让我们可以一点点增加对场的了解。

the conditions there. The field here and now depends on the field in the immediate neighbourhood at a time just past. The equations allow us to predict what will happen a little farther in space and a little later in time, i f we know what happens here and now. They allow us to increase our knowledge of the field by small steps.

通过把这些非常小的步长相加，我们可以从远处发生的事情推断出这里发生的事情。相反，在牛顿理论中，只有连接遥远事件的大步长才是允许的。奥斯特和法拉第的实验可以从麦克斯韦理论中恢复，但只能通过把每个小步长相加，每个小步长都受麦克斯韦方程的支配。

We can deduce what happens here from that which happened far away by the summation of these very small steps. In Newton’s theory, on the contrary, only big steps connecting distant events are permissible. The experiments of Oersted and Faraday can be regained from M axwell’s theory, but only by the summation of small steps each o f which is governed by Maxwell’s equations.

对麦克斯韦方程组进行更彻底的数学研究表明，可以得出新的和真正出乎意料的结论，并且可以在更高的水平上对整个理论进行检验，因为理论后果现在具有定量特征，并通过一系列逻辑论证来揭示。

A more thorough mathematical study of Maxwell’s equations shows that new and really unexpected conclusions can be drawn and the whole theory submitted to a test on a much higher level, because the theoretical consequences are now o f a quantitative character and are revealed by a whole chain o f logical arguments.

让我们再想象一个理想化的实验。一个带电的小球体在某种外部影响下被迫像钟摆一样快速有节奏地振荡。根据我们已经掌握的场的变化知识，我们该如何用场语言描述这里发生的一切？

Let us again imagine an idealized experiment. A small sphere with an electric charge is forced, by some external influence, to oscillate rapidly and in a rhythmical way, like a pendulum. With the knowledge we already have o f the changes o f the field, how shall we describe everything that is going on here, in the field language?

电荷的振荡产生变化的电场。这总是伴随着变化的磁场。如果在附近放置一根形成闭合电路的导线，则变化的磁场

The oscillation o f the charge produces a changing electric field. This is always accompanied by a changing magnetic field. I f a wire forming a closed circuit is placed in the vicinity, then again the changing

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磁场将伴随电路中的电流。所有这些只是已知事实的重复，但对麦克斯韦方程的研究使人们对振荡电荷的问题有了更深入的了解。通过对麦克斯韦方程的数学推导，我们可以检测出振荡电荷周围的场的特性、其在源附近和远处的结构以及它随时间的变化。

magnetic field will be accompanied by an electric current in the circuit. A ll this is merely a repetition o f known facts, but the study o f Maxwell’s equations gives a much deeper insight into the problem o f the oscillating electric charge. By mathematical deduction from M axwell’s equations we can detect the character o f the field surrounding an oscillating charge, its structure near and far from the source and its change with time.

这种推论的结果就是 电磁波 。能量从以一定的速度穿过空间的振荡电荷辐射出来；但能量的转移，即状态的运动，是所有波现象的特征。

The outcome o f such deduction is the electromagnetic wave. Energy radiates from the oscillating charge travelling with a definite speed through space; but a transference o f energy, the motion o f a state, is characteristic o f all wave phenomena.

我们已经考虑过不同类型的波。有由脉动球体引起的纵波，其中密度的变化通过介质传播。有果冻状介质，横波在其中传播。果冻的变形是由球体的旋转引起的，并穿过介质。在电磁波的情况下，现在传播的是什么样的变化？只是电磁场的变化！电场的每次变化都会产生磁场；该磁场的每次变化都会产生电场；每次变化……，等等。由于场代表能量，所有这些以一定的速度在空间中传播的变化都会产生波。根据理论推论，电力线和磁力线总是位于垂直于传播方向的平面上。波

Different types o f waves have already been considered. There was the longitudinal wave caused by the pulsating sphere, where the changes of density were propagated through the medium. There was the jelly-like medium in which the transverse wave spread. A deformation of the jelly, caused by the rotation of the sphere, moved through the medium. W hat kind of changes are now spreading in the case of an electromagnetic wave? Ju st the changes o f an electromagnetic fie ld ! Every change of an electric field produces a magnetic field; every change o f this magnetic field produces an electric field; every change o f . . . , and so on. As field represents energy, all these changes spreading out in space, with a definite velocity, produce a wave. The electric and magnetic lines o f force always lie, as deduced from the theory, on planes perpendicular to the direction o f propagation. The wave

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因此，产生的磁场是横向的。我们从奥斯特和法拉第的实验中形成的场的图像的原始特征仍然保留，但我们现在认识到它具有更深的含义。

produced is, therefore, transverse. The original features of the picture of the field we formed from Oersted’s and Faraday’s experiments are still preserved, but we now recognize that it has a deeper meaning.

电磁波在空旷的空间中传播。

The electromagnetic wave spreads in empty space.

这又是该理论的结果。如果振荡电荷突然停止移动，那么它的场就会变成静电场。但振荡产生的一系列波会继续传播。波独立存在，它们的变化历史可以像任何其他物质对象一样被追踪。

This, again, is a consequence of the theory. I f the oscillating charge suddenly ceases to move, then its field becomes electrostatic. But the series o f waves created by the oscillation continues to spread. The waves lead an independent existence and the history of their changes can be followed just as that of any other material object.

我们知道，电磁波在空间中以一定的速度传播，并随时间变化，这一图像之所以遵循麦克斯韦方程，只是因为它们描述了空间中任意一点和任意瞬间的电磁场结构。

We understand that our picture o f an electromagnetic wave, spreading with a certain velocity in space and changing in time, follows from Maxwell’s equations only because they describe the structure o f the electromagnetic field at any point in space and for any instant.

还有一个非常重要的问题，电磁波在空旷的空间中传播的速度是多少？理论在一些与波的实际传播无关的简单实验数据的支持下给出了明确的答案：电磁波的速度 等于光速 。

There is another very important question. With what speed does the electromagnetic wave spread in empty space? The theory, with the support o f some data from simple experiments having nothing to do with the actual propagation of waves, gives a clear answer: the velocity of an electromagnetic wave is equal to the velocity of light .

奥斯特和法拉第的实验构成了麦克斯韦定律的基础。迄今为止，我们所有的成果都来自对这些定律的仔细研究，这些定律以场语言表达。电磁波以场的形式传播的理论发现

Oersted’s and Faraday’s experiments formed the basis on which Maxwell’s laws were built. A ll our results so far have come from a careful study of these laws, expressed in the field language. The theoretical discovery o f an electromagnetic wave spreading with

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光速是科学史上最伟大的成就之一。

the speed o f light is one o f the greatest achievements in the history of science.

实验证实了理论的预测。

Experiment has confirmed the prediction o f theory.

五十年前，赫兹首次证明了电磁波的存在，并通过实验证实了电磁波的速度等于光速。如今，数百万人证明了电磁波的发送和接收。他们的仪器比赫兹使用的仪器复杂得多，可以探测到距离波源数千英里而不是几码远的波的存在。

Fifty years ago, Hertz proved, for the first time, the existence of electromagnetic waves and confirmed experimentally that their velocity is equal to that of light. Nowadays, millions o f people demonstrate that electromagnetic waves are sent and received. Their apparatus is far more complicated than that used by Hertz and detects the presence o f waves thousands of miles from their sources instead of only a few yards.

田野与以太

F I E L D A N D E T H E R

电磁波是横向波，在空旷的空间中以光速传播。

The electromagnetic wave is a transverse one and is propagated with the velocity o f light in empty space.

它们的速度相同这一事实表明光学现象和电磁现象之间存在密切的关系。

The fact that their velocities are the same suggests a close relationship between optical and electromagnetic phenomena.

当我们必须在粒子理论和波动理论之间做出选择时，我们决定选择波动理论。光的衍射是影响我们决定的最有力论据。但我们不会因为假设光波 是电磁波而与任何光学事实的解释相矛盾。相反，我们还可以得出其他结论。如果事实确实如此，那么物质的光学和电学特性之间一定存在某种联系，而这些联系可以从该理论中推导出来。事实上，这种结论确实可以得出

When we had to choose between the corpuscular and the wave theory, we decided in favour o f the wave theory. The diffraction of light was the strongest argument influencing our decision. But we shall not contradict any of the explanations of the optical facts by also assuming that the light wave is an electromagnetic one. O n the contrary, still other conclusions can be drawn. I f this is really so, then there must exist some connection between the optical and electrical properties o f matter that can be deduced from the theory. The fact that conclusions o f this kind can really be drawn

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并且它们经得起实验的检验，这是支持光的电磁理论的重要论据。

and that they stand the test of experiment is an essential argument in favour of the electromagnetic theory of light.

这一伟大成果归功于场论。两个看似不相关的科学分支被同一个理论所涵盖。同一个麦克斯韦方程既描述了电感应，又描述了光折射。如果我们的目标是借助一个理论来描述曾经发生或可能发生的一切，那么光学和电学的结合无疑是向前迈出的一大步。从物理角度来看，普通电磁波和光波之间的唯一区别就是波长：对于人眼探测到的光波来说，波长非常小，而对于无线电接收器探测到的普通电磁波来说，波长很大。

This great result is due to the field theory. Two apparently unrelated branches of science are covered by the same theory. The same Maxwell’s equations describe both electric induction and optical refraction. I f it is our aim to describe everything that ever happened or may happen with the help of one theory, then the union of optics and electricity is, undoubtedly, a very great step forward. From the physical point of view, the only difference between an ordinary electromagnetic wave and a light wave is the wave-length: this is very small for light waves, detected by the human eye, and great for ordinary electromagnetic waves, detected by a radio receiver.

旧的机械观试图将自然界中的所有事件归结为物质粒子之间的力作用。电流体的第一个朴素理论就是以这种机械观为基础的。对于十九世纪早期的物理学家来说，场并不存在。对他来说，只有物质及其变化才是真实的。他试图仅通过直接指代两个电荷的概念来描述两个电荷的作用。

The old mechanical view attempted to reduce all events in nature to forces acting between material particles. U pon this mechanical view was based the first naïve theory of the electric fluids. The field did not exist for the physicist of the early years of the nineteenth century. For him only substance and its changes were real. He tried to describe the action of two electric charges only by concepts referring directly to the two charges.

起初，场的概念不过是机械理解现象的一种手段。在新的场语言中，描述两个电荷之间的场，而不是电荷本身，才是

In the beginning, the field concept was no more than a means of facilitating the understanding of phenomena from the mechanical point o f view. In the new field language it is the description of the field between the two charges, and not the charges themselves, which is

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理解它们的作用至关重要。人们对新概念的认识稳步增长，直到物质被场所掩盖。人们意识到物理学中发生了一些非常重要的事情。

essential for an understanding of their action. The recognition o f the new concepts grew steadily, until substance was overshadowed by the field. It was realized that something of great importance had happened in physics.

一个新的现实被创造出来，一个机械描述中没有容身之处的新概念。

A new reality was created, a new concept for which there was no place in the mechanical description.

经过一番努力，场的概念逐渐在物理学中占据了主导地位，并一直是基本物理概念之一。对于现代物理学家来说，电磁场就像他坐的椅子一样真实。

Slowly and by a struggle the field concept established for itself a leading place in physics and has remained one of the basic physical concepts. The electromagnetic field is, for the modern physicist, as real as the chair on which he sits.

但是，认为新场观将科学从旧电流体理论的错误中解放出来，或者认为新理论摧毁了旧理论的成就，这是不公平的。新理论既展示了旧理论的优点，也展示了旧理论的局限性，并使我们能够从更高的层次重新获得旧概念。这不仅适用于电流体和场理论，也适用于物理理论的所有变化，无论它们看起来多么具有革命性。在我们的例子中，我们仍然可以在麦克斯韦理论中找到电荷的概念，尽管电荷仅被理解为电场的来源。库仑定律仍然有效，并包含在麦克斯韦方程中，从中可以推导出它的众多后果之一。只要研究了旧理论有效范围内的事实，我们仍然可以应用旧理论。但我们也可以应用新理论，因为所有已知事实都包含在其有效范围内。

But it would be unjust to consider that the new field view freed science from the errors o f the old theory of electric fluids or that the new theory destroys the achievements of the old. The new theory shows the merits as well as the limitations o f the old theory and allows us to regain our old concepts from a higher level. This is true not only for the theories of electric fluids and field, but for all changes in physical theories, however revolutionary they may seem. In our case, we still find, for example, the concept o f the electric charge in Maxwell’s theory, though the charge is understood only as a source o f the electric field. Coulomb’s law is still valid and is contained in Maxwell’s equations from which it can be deduced as one of the many consequences. We can still apply the old theory, whenever facts within the region of its validity are investigated. But we may as well apply the new theory, since all the known facts are contained in the realm o f its validity.

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打个比方，我们可以说，创造一种新理论并不像摧毁一个旧谷仓，然后在其原址上建起一座摩天大楼。它更像是攀登一座山峰，获得新的、更广阔的视野，发现我们的起点和其丰富的环境之间意想不到的联系。但我们出发的那个点仍然存在，我们可以看到，尽管它看起来更小，并且只是我们在冒险攀登过程中克服障碍所获得的广阔视野的一小部分。

To use a comparison, we could say that creating a new theory is not like destroying an old barn and erecting a skyscraper in its place . I t is rather like climbing a mountain, gaining new and wider views, discovering unexpected connections between our starting-point and its rich environment. But the point from which we started out still exists and can be seen, although it appears smaller and forms a tiny part o f our broad view gained by the mastery of the obstacles on our adventurous way up.

事实上，人们花了很长时间才认识到麦克斯韦理论的全部内容。起初，人们认为场可以稍后借助以太进行机械解释。当人们意识到这个计划无法实现时，场论的成就已经变得太引人注目和重要，以至于不能用机械教条来代替它。另一方面，设计以太的机械模型的问题似乎变得越来越无趣，而且由于假设的强制和人为性质，结果越来越令人沮丧。

It was, indeed, a long time before the full content o f Maxwell’s theory was recognized. The field was at first considered as something which might later be interpreted mechanically with the help o f ether. By the time it was realized that this programme could not be carried out, the achievements o f the field theory had already become too striking and important for it to be exchanged for a mechanical dogma. O n the other hand, the problem of devising the mechanical model o f ether seemed to become less and less interesting and the result, in view of the forced and artificial character of the assumptions, more and more discouraging.

我们唯一的出路似乎是理所当然地认为空间具有传输电磁波的物理特性，而不必太在意这个说法的含义。我们可能仍然使用以太这个词，但只用来表达空间的某种物理特性。以太这个词在科学的发展中已经多次改变了它的含义。现在它不再代表一种由电磁波组成的介质。

O ur only way out seems to be to take for granted the fact that space has the physical property o f transmitting electromagnetic waves, and not to bother too much about the meaning o f this statement. We may still use the word ether, but only to express some physical property of space. This word ether has changed its meaning many times in the development o f science. A t the moment it no longer stands for a medium built up

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粒子。它的故事还远没有结束，相对论将把它继续下去。

of particles. Its story, by no means finished, is continued by the relativity theory.

THEMECHANICALS脚手架

T H E M E C H A N I C A L S C A F F O L D

讲到这个阶段，我们必须回到开头，回到伽利略的惯性定律。我们再次引用：

O n reaching this stage of our story, we must turn back to the beginning, to Galileo’s law of inertia. We quote once more:

任何物体都会保持其静止状态或沿直线的匀速运动状态，除非受到施加在其上的力而被迫改变该状态。

Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.

一旦理解了惯性的概念，人们就会想知道关于它还有什么可以说的。尽管这个问题已经被彻底讨论过了，但它绝非穷尽。

Once the idea of inertia is understood, one wonders what more can be said about it. Although this problem has already been thoroughly discussed, it is by no means exhausted.

设想一位严肃的科学家相信惯性定律可以通过实际实验得到证实或证伪。他沿着水平桌面推动小球，尽量消除摩擦。他注意到，随着桌面和小球变得更光滑，运动变得更均匀。就在他即将宣布惯性原理时，突然有人对他开了个玩笑。我们的物理学家在一个没有窗户的房间里工作，与外界没有任何联系。这个爱开玩笑的人安装了一些装置，使他能够使整个房间绕着通过其中心的轴快速旋转。旋转一开始，物理学家就有了新的和意想不到的体验。一直匀速运动的球体

Imagine a serious scientist who believes that the law of inertia can be proved or disproved by actual experiments. H e pushes small spheres along a horizontal table, trying to eliminate friction so far as possible. H e notices that the motion becomes more uniform as the table and the spheres are made smoother. Ju st as he is about to proclaim the principle o f inertia, someone suddenly plays a practical joke on him. O ur physicist works in a room without windows and has no communication whatever with the outside world. The practical joker installs some mechanism which enables him to cause the entire room to rotate quickly on an axis passing through its centre. As soon as the rotation begins, the physicist has new and unexpected experiences. The sphere which has been moving uniformly

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试图尽可能远离中心，靠近房间的墙壁。他自己感觉到一股奇怪的力量把他推向墙壁。他体验到的感觉和任何在火车或汽车上快速转弯，甚至在旋转木马上行驶的人一样。他之前的所有结果都化为泡影。

tries to get as far away from the centre and as near to the walls o f the room as possible. H e himself feels a strange force pushing him against the wall. H e experiences the same sensation as anyone in a train or car travelling fast round a curve, or even more, on a rotating merry-go-round. A ll his previous results go to pieces.

我们的物理学家必须抛弃惯性定律，抛弃所有机械定律。惯性定律是他的出发点；如果这一点改变，他所有进一步的结论也都会改变。一个注定要一生待在旋转房间并在那里进行所有实验的观察者，他的力学定律将与我们的不同。另一方面，如果他带着深厚的知识和对物理学原理的坚定信念进入房间，他对力学明显失效的解释将是假设房间在旋转。通过机械实验，他甚至可以确定房间是如何旋转的。

O ur physicist would have to discard, with the law of inertia, all mechanical laws. The law of inertia was his starting-point; if this is changed, so are all his further conclusions. A n observer destined to spend his whole life in the rotating room, and to perform all his experiments there, would have laws o f mechanics differing from ours. If, on the other hand, he enters the room with a profound knowledge and a firm belief in the principles of physics, his explanation for the apparent breakdown of mechanics would be the assumption that the room rotates. By mechanical experiments he could even ascertain how it rotates.

我们为什么要对旋转房间中的观察者如此感兴趣呢？原因很简单，因为我们在地球上，在某种程度上处于相同的位置。

Why should we take so much interest in the observer in his rotating room? Simply because we, on our earth, are to a certain extent in the same position.

从哥白尼时代起，我们就知道地球绕地轴自转并围绕太阳运转。

Since the time of Copernicus we have known that the earth rotates on its axis and moves around the sun.

即使是这个简单的想法，每个人都很清楚，但科学的进步也影响到了它。不过，我们暂时把这个问题搁置一边，接受哥白尼的

Even this simple idea, so clear to everyone, was not left untouched by the advance o f science. But let us leave this question for the time being and accept Copernicus’

观点。如果我们旋转的观察者无法证实力学定律，那么地球上的我们也应该无法证实。但地球的自转是

point of view. I f our rotating observer could not confirm the laws o f mechanics, we on our earth, should also be unable to do so. But the rotation of the earth is

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速度比较慢，所以效果不是很明显。但是，有许多实验显示出对力学定律的微小偏离，它们的一致性可以看作是地球自转的证据。

comparatively slow, so that the effect is not very distinct. Nevertheless, there are many experiments which show a small deviation from the mechanical laws, and their consistency can be regarded as proof of the rotation of the earth.

不幸的是，我们无法将自己置于太阳和地球之间，在那里证明惯性定律的确切有效性并观察地球的旋转。这只能在想象中实现。我们所有的实验都必须在我们被迫生活的地球上进行。同样的事实往往可以用更科学的方式表达： 地球是我们的坐标 系。

Unfortunately we cannot place ourselves between the sun and the earth, to prove there the exact validity of the law of inertia and to get a view of the rotating earth. This can be done only in imagination. A ll our experiments must be performed on the earth on which we are compelled to live. The same fact is often expressed more scientifically: the earth is our co-ordinate system.

为了更清楚地说明这些词的含义，让我们举一个简单的例子。我们可以随时预测从塔上扔下的石头的位置，并通过观察来证实我们的预测。如果将量杆放在塔旁，我们可以预测在任何给定时刻下落的物体将与量杆上的哪个标记重合。显然，塔和秤不能由橡胶或任何在实验过程中会发生变化的材料制成。事实上，原则上，与地面牢固连接的不可改变的秤和一台好钟就是我们进行实验所需要的一切。如果我们有这些，我们不仅可以忽略塔的建筑，还可以忽略它的存在。上述假设都是微不足道的，通常不会在此类实验的描述中具体说明。但这种分析表明，在我们国家的每个实验中都隐藏着多少假设——

To show the meaning of these words more clearly, let us take a simple example. We can predict the position, at any time, o f a stone thrown from a tower, and confirm our prediction by observation. I f a measuring-rod is placed beside the tower, we can foretell with what mark on the rod the falling body will coincide at any given moment. The tower and scale must, obviously, not be made of rubber or any other material which would undergo any change during the experiment. In fact, the unchangeable scale, rigidly connected with the earth, and a good clock are all we need, in principle, for the experiment. I f we have these, we can ignore not only the architecture of the tower, but its very presence. The foregoing assumptions are all trivial and not usually specified in descriptions of such experiments. But this analysis shows how many hidden assumptions there are in every one of our state-

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在我们的例子中，我们假设存在一根刚性杆和一个理想的时钟，没有它们，就不可能检验伽利略的落体定律。有了这个简单但基本的物理装置，一根杆和一个时钟，我们可以在一定程度上准确地证实这一力学定律。经过仔细的执行，这个实验揭示了由于地球自转而导致的理论与实验之间的差异，或者换句话说，由于这里所制定的力学定律在与地球刚性连接的坐标系中并不严格有效。

ments. In our case, we assumed the existence of a rigid bar and an ideal clock, without which it would be impossible to check Galileo’s law for falling bodies. With this simple but fundamental physical apparatus, a rod and a clock, we can confirm this mechanical law with a certain degree of accuracy. Carefully performed, this experiment reveals discrepancies between theory and experiment due to the rotation of the earth or, in other words, to the fact that the laws of mechanics, as here formulated, are not strictly valid in a co-ordinate system rigidly connected with the earth.

在所有机械实验中，无论何种类型，我们都必须确定物质点在某个确定时间的位置，就像上述落体实验一样。但位置必须始终相对于某个东西来描述，就像前例中相对于塔和秤来描述一样。我们必须有所谓的某种 参考系，即机械脚手架，才能确定物体的位置。在描述城市中物体和人的位置时，街道和大道构成了我们所参考的框架。

In all mechanical experiments, no matter of what type, we have to determine positions of material points at some definite time, just as in the above experiment with a falling body. But the position must always be described with respect to something, as in the previous case to the tower and the scale. We must have what we call some frame of reference, a mechanical scaffold, to be able to determine the positions of bodies. In describing the positions of objects and men in a city, the streets and avenues form the frame to which we refer.

到目前为止，我们在引用力学定律时还没有费心描述框架，因为我们恰好生活在地球上，在任何特殊情况下，固定一个与地球牢固连接的参考框架都没有困难。这个由刚性不变的物体构成的框架，我们参考它来进行所有的观察，它被称为 坐标系。由于这个表达式会经常使用，我们将简单地写成 CS

So far we have not bothered to describe the frame when quoting the laws of mechanics, because we happen to live on the earth and there is no difficulty in any particular case in fixing a frame o f reference, rigidly connected with the earth. This frame, to which we refer all our observations, constructed of rigid unchangeable bodies, is called the co-ordinate system. Since this expression will be used very often, we shall simply write C.S.

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我们所有的身体状况 1

A ll our physical statem 1

到目前为止，还没有

ents thus far have lacked

我们没有注意到所有观察都必须在某个 CS 中进行的事实。我们没有描述该 CS 的结构，而是忽略了它的存在。例如，当我们写“物体匀速运动……”时，我们实际上应该写成“物体相对于选定的 CS 匀速运动……”。我们在旋转室中的经验告诉我们，机械实验的结果可能取决于所选的 CS。

something. We took no notice of the fact that all observations must be made in a certain C.S. Instead of describing the structure of this C.S., we just ignored its existence. For example, when we wrote “ a body moves uniformly. . . ” we should really have written, “ a body moves uniformly, relative to a chosen C .S . ....” O ur experience with the rotating room taught us that the results of mechanical experiments may depend on the C.S. chosen.

如果两个坐标系相对旋转，那么力学定律就不能同时适用于这两个坐标系。如果构成其中一个坐标系的游泳池水面是水平的，那么在另一个坐标系中，类似游泳池的水面将呈现弯曲的形状，就像任何用勺子搅拌咖啡的人一样。

I f two C.S. rotate with respect to each other, then the laws of mechanics cannot be valid in both. I f the surface of the water in a swimming pool, forming one of the co-ordinate systems, is horizontal, then in the other the surface of the water in a similar swimming pool takes the curved form similar to anyone who stirs his coffee with a spoon.

在阐述力学的主要线索时，我们忽略了一个重要点。我们没有说明它们适用于哪个坐标系。因此，整个经典力学都悬而未决，因为我们不知道它指的是哪个坐标系。不过，我们暂时先忽略这个困难。我们将做出一个稍微不正确的假设，即在每个与地球刚性连接的坐标系中，经典力学定律都是有效的。这样做是为了固定坐标系

When formulating the principal clues of mechanics we omitted one important point. We did not state for which C.S. they are vali d . For this reason, the whole of classical mechanics hangs in mid-air since we do not know to which frame it refers. Let us, however, pass over this difficulty for the moment. We shall make the slightly incorrect assumption that in every C.S. rigidly connected with the earth the laws of classical mechanics are valid. This is done in order to fix the C.S.

并使我们的陈述明确。尽管我们关于地球是一个合适的参考系的说法并不完全正确，但我们暂时接受它。

and to make our statements definite. Although our statement that the earth is a suitable frame of reference is not wholly correct, we shall accept it for the present.

因此，我们假设存在一个 CS

We assume, therefore, the existence of one C.S. for

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力学定律适用的坐标系。这是唯一的坐标系吗？假设我们有一个相对于地球运动的坐标系，比如火车、轮船或飞机。力学定律对这些新坐标系适用吗？我们确切地知道它们并不总是适用，例如火车转弯、轮船在暴风雨中颠簸或飞机尾旋的情况。让我们从一个简单的例子开始。一个坐标系相对于我们的“良好”坐标系均匀运动，即力学定律适用的坐标系。例如，一列理想的火车或轮船沿着直线平稳行驶，速度保持不变。我们从日常经验中知道这两个系统都是“良好的”，在均匀运动的火车或轮船上进行的物理实验将得到与地球上完全相同的结果。但是，如果火车停了下来，或者突然加速，或者海面波涛汹涌，就会发生奇怪的事情。在火车上，行李架上的行李会掉下来；在船上，桌椅被抛来抛去，乘客晕船。从物理角度来看，这仅仅意味着力学定律不能应用于这些 CS，它们是“坏”CS

which the laws of mechanics are valid. Is this the only one? Suppose we have a C.S. such as a train, a ship or an aeroplane moving relative to our earth. W ill the laws of mechanics be valid for these new C.S.? We know definitely that they are not always valid, as for instance in the case of a train turning a curve, a ship tossed in a storm or an aeroplane in a tail spin. Let us begin with a simple example. A C.S. moves uniformly, relative to our “ good” C.S., that is, one in which the laws of mechanics are valid. For instance, an ideal train or a ship sailing with delightful smoothness along a straight line and with a never-changing speed. We know from everyday experience that both systems will be “ good” , that physical experiments performed in a uniformly moving train or ship will give exactly the same results as on the earth. But, if the train stops, or accelerates abruptly, or if the sea is rough, strange things happen. In the train, the trunks fall off the luggage racks; on the ship, tables and chairs are thrown about and the passengers become seasick. From the physical point of view this simply means that the laws of mechanics cannot be applied to these C.S., that they are “ ba d” C.S.

这个结果可以用所谓的 伽利略 相对性原理来表达： 如果力学定律在一个坐标系中成立，那么它们在相对于第一个坐标系匀速运动的任何其他 坐标系中也成立。

This result can be expressed by the so-called Galilean relativity principle: i f the laws o f mechanics are valid in one C.S., then they are valid in any other C.S. moving uniformly relative to the first.

如果有两个坐标系相对非均匀运动，那么力学定律就不可能同时适用于这两个坐标系。“好的”坐标系，即

I f we have two C.S. moving non-uniformly, relative to each other, then the laws of mechanics cannot be valid in both. “ G o o d ” co-ordinate systems, that is,

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那些符合力学定律的物体，我们称之为 惯性系统。 惯性系统是否存在，这个问题至今仍未解决。但如果有一个这样的系统，那么就会有无数个这样的系统。每个相对于初始坐标系匀速运动的坐标系，也是一个惯性坐标系

those for which the laws of mechanics are valid, we call inertial systems. The question as to whether an inertial system exists at all is still unsettled. But if there is one such system, then there is an infinite number of them. Every C.S. moving uniformly, relative to the initial one, is also an inertial C.S.

让我们考虑两个坐标系从已知位置出发并以已知速度相对于另一个坐标系匀速运动的情况。喜欢具体图像的人可以放心地想象一艘船或一列火车相对于地球运动。力学定律可以在地球上、在匀速运动的火车或船上以同样的精度通过实验得到证实。但是，如果两个系统的观察者开始从不同坐标系的角度讨论对同一事件的观察，就会出现一些困难。每个人都想把对方的观察结果翻译成自己的语言。再举一个简单的例子：从两个坐标系——地球和匀速运动的火车——观察到一个粒子的相同运动。

Let us consider the case of two C.S. starting from a known position and moving uniformly, one relative to the other, with a known velocity. O ne who prefers concrete pictures can safely think of a ship or a train moving relative to the earth. The laws o f mechanics can be confirmed experimentally with the same degree of accuracy, on the earth or in a train or on a ship moving uniformly. But some difficulty arises if the observers o f two systems begin to discuss observations of the same event from the point of view of their different C.S. Each would like to translate the other’s observations into his own language. Again a simple example: the same motion of a particle is observed from two C.S.— the earth and a train moving uniformly.

这些都是惯性的。如果知道某一时刻两个坐标系的相对速度和位置，那么知道在一个坐标系中观察到什么就足以找出在另一个坐标系中观察到什么了吗？对于事件的描述来说，最重要的是知道如何从一个坐标系转到另一个坐标系，因为两个坐标系是等价的，并且都同样适合描述自然界中的事件。事实上，知道观察者在一个坐标系中获得的结果就足以知道观察者在另一个坐标系中获得的结果。

These are both inertial. Is it sufficient to know what is observed in one C.S. in order to find out what is observed in the other, if the relative velocities and positions of the two C.S. at some moment are known? It is most essential, for a description of events, to know how to pass from one C.S. to another, since both C.S. are equivalent and both equally suited for the description of events in nature. Indeed, it is quite enough to know the results obtained by an observer in one C.S. to know those obtained by an observer in the other.

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让我们更抽象地考虑这个问题，不考虑轮船或火车。为简化问题，我们只研究沿直线的运动。那么，我们有一根带有刻度的刚性杆和一只好钟。在简单的直线运动情况下，刚性杆代表一个坐标系，就像伽利略实验中塔上的刻度一样。在直线运动的情况下，将坐标系想象成一根刚性杆，在空间任意运动的情况下，不考虑塔、墙、街道等，将坐标系想象成一个由平行和垂直杆构成的刚性脚手架，总是更简单、更好。假设在最简单的情况下，我们有两个坐标系，即两根刚性杆；我们将一根画在另一根上方，分别称它们为“上”坐标系和“下”坐标系。我们假设两个坐标系以确定的速度相对于彼此移动，因此一个沿着另一个滑动。可以安全地假设两根杆都是无限长的，有起始点但没有终点。对于两个 CS 来说，一个时钟就足够了，因为两者的时间流是相同的。

Let us consider the problem more abstractly, without ship or train. To simplify matters we shall investigate only motion along straight lines. We have, then, a rigid bar with a scale and a good clock. The rigid bar represents, in the simple case o f rectilinear motion, a C.S. just as did the scale on the tower in Galileo’s experiment. It is always simpler and better to think of a C.S. as a rigid bar in the case o f rectilinear motion and a rigid scaffold built of parallel and perpendicular rods in the case o f arbitrary motion in space, disregarding towers, walls, streets, and the like. Suppose we have, in our simplest case, two C.S., that is, two rigid rods; we draw one above the other and call them respectively the “ upper” and “ lower” C.S. We assume that the two C.S. move with a definite velocity relative to each other, so that one slides along the other. It is safe to assume that both rods are of infinite length and have initial points but no end-points. O ne clock is sufficient for the two C.S., for the time flow is the same for both.

当我们开始观察时，两根杆的起点重合。此时，质点的位置在两个坐标系中用相同的数字来表示。质点与杆上刻度上的一个点重合，从而给出一个确定该质点位置的数字。但是，如果杆相对彼此均匀移动，则对应于位置的数字将在一段时间（例如一秒）后有所不同。考虑静止在上杆上的质点。确定其在上坐标系上位置的数字不会随时间而变化。

When we begin our observation the starting-points of the two rods coincide. The position of a material point is characterized, at this moment, by the same number in both C.S. The material point coincides with a point on the scale on the rod, thus giving us a number determining the position of this material point. But, if the rods move uniformly, relative to each other, the numbers corresponding to the positions will be different after some time, say, one second. Consider a material point resting on the upper rod. The number determining its position on the upper C.S. does not change with time.

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但下杆对应的数字会发生变化。我们不应该说“与点的位置对应的数字”，而应该简单地说“ 点的坐标” 。因此，从我们的图中可以看出，虽然下面的句子听起来很复杂，但它是正确的，表达的是非常简单的东西。

But the corresponding number for the lower rod will change. Instead o f “ the number corresponding to a position o f the point” , we shall say briefly, the coordinate o f a point. Thus we see from our drawing that although the following sentence sounds intricate, it is nevertheless correct and expresses something very simple.

下 CS 中某个点的坐标等于其在上 CS 中的坐标加上上 CS 原点相对于下 CS 的坐标

The co-ordinate of a point in the lower C.S. is equal to its co-ordinate in the upper C.S. plus the co-ordinate of the origin of the upper C.S. relative to the lower C.S.

重要的是，如果我们知道粒子在另一坐标系中的位置，我们总能计算出粒子在某一坐标系中的位置。为此，我们必须知道所讨论的两个坐标系在每一时刻的相对位置。虽然这一切听起来很深奥，但实际上非常简单，几乎不值得如此详细地讨论，除非我们以后会发现它很有用。

The important thing is that we can always calculate the position o f a particle in one C.S. if we know the position in the other. For this purpose we have to know the relative positions of the two co-ordinate systems in question at every moment. Although all this sounds learned, it is, really, very simple and hardly worth such detailed discussion, except that we shall find it useful later.

值得注意的是，确定一个点的位置和确定一个事件的时间是不同的。每个观察者都有自己的杆，构成他的坐标系，但对他们来说只有一个时钟。

It is worth our while to notice the difference between determining the position o f a point and the time o f an event. Every observer has his own rod which forms his C.S., but there is only one clock for them all.

时间是“绝对的”，对于所有 CS 中的所有观察者来说，时间都以相同的方式流动

Tim e is something “ absolute” which flows in the same way for all observers in all C.S.

现在再举一个例子。一名男子以每小时三英里的速度沿着一艘大船的甲板漫步。

Now another example. A man strolls with a velocity of three miles per hour along the deck o f a large ship.

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这是他相对于飞船的速度，或者换句话说，相对于与飞船刚性连接的 CS 的速度。

This is his velocity relative to the ship, or, in other words, relative to a C.S. rigidly connected with the ship.

如果船相对于岸的速度为每小时三十英里，并且人与船的匀速速度方向相同，那么婴儿车相对于岸上的观察者的速度就是每小时三十三英里，相对于船的速度就是每小时三英里。我们可以更抽象地表述这一事实：移动物质点相对于下部坐标系的速度等于相对于上部坐标系的速度加上或减去上部坐标系相对于下部坐标系的速度，这取决于速度方向相同还是相反。因此，如果我们知道两个坐标系的相对速度，我们就可以始终将位置和速度从一个坐标系变换到另一个坐标系。位置或坐标和速度就是不同坐标系中不同的量，它们通过某些（在本例中是非常简单的） 变换定律结合在一起。

I f the velocity of the ship is thirty miles per hour relative to the shore, and if the uniform velocities of man and ship both have the same direction, then the velocity of the stroller will be thirty-three miles per hour relative to an observer on the shore, or three miles per hour relative to the ship. We can formulate this fact more abstractly: the velocity of a moving material point, relative to the lower C.S., is equal to that relative to the upper C.S. plus or minus the velocity o f the upper C.S. relative to the lower, depending upon whether the velocities have the same or opposite directions. We can, therefore, always transform not only positions, but also velocities from one C.S. to another if we know the relative velocities of the two C.S. The positions, or co-ordinates, and velocities are examples of quantities which are different in different C.S. bound together by certain, in this case very simple, transformation laws.

然而，存在一些量，它们在两个 CS 中是相同的，并且不需要变换定律。以上杆上的两个固定点为例，它们之间的距离不是固定的一个，而是固定的两个点。这个距离是两个点的坐标差。为了找到位置

There exist quantities, however, which are the same in both C.S. and for which no transformation laws are needed. Take as an example not one, but two fixed points on the upper rod and consider the distance between them. This distance is the difference in the co-ordinates of the two points. To find the positions

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两个点相对于不同 CS 的距离，我们必须使用变换定律。但在构造两个位置的差异时，不同 CS 的贡献会相互抵消并消失，从图中可以看出。我们必须增加和减去两个 CS 原点之间的距离。因此，两个点的距离是 不变的，即与 CS 的选择无关

of two points relative to different C.S., we have to use transformation laws. But in constructing the differences of two positions the contributions due to the different C.S. cancel each other and disappear, as is evident from the drawing. We have to add and subtract the distance between the origins of two C.S. The distance of two points is, therefore, invariant, that is, independent of the choice o f the C.S.

下一个与坐标系无关的量的例子是速度变化，这是我们在力学中熟悉的一个概念。同样，从两个坐标系观察到沿直线运动的质点，对于每个坐标系中的观察者来说，它的速度变化是两个速度之间的差值，当计算出差值时，由于两个坐标系的相对运动是均匀的，速度变化就消失了。因此，速度变化是一个不变量，当然，前提是我们两个坐标系的相对运动是均匀的。否则，两个坐标系中的速度变化将有所不同，这种差异是由代表我们坐标系的两个杆的相对运动速度变化引起的。

The next example of a quantity independent of the C.S. is the change of velocity, a concept familiar to us from mechanics. Again, a material point moving along a straight line is observed from two C.S. Its change o f velocity is, for the observer in each C.S., a difference between two velocities, and the contribution due to the uniform relative motion of the two C.S. disappears when the difference is calculated. Therefore, the change of velocity is an invariant, though only, o f course, on condition that the relative motion o f our two C.S. is uniform. Otherwise, the change o f velocity would be different in each o f the two C.S., the difference being brought in by the change o f velocity o f the relative motion o f the two rods, representing our co-ordinate systems.

现在来看最后一个例子！我们有两个质点，它们之间作用的力只取决于

Now the last example ! We have two material points, with forces acting between them which depend only

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距离不变。在直线运动的情况下，距离不变，因此力也是不变的。

on the distance. In the case o f rectilinear motion, the distance, and therefore the force as well, is invariant.

因此，将力与速度变化联系起来的牛顿定律在两个坐标系中都有效。我们再次得出一个日常经验证实的结论：如果力学定律在一个坐标系中有效，那么它们在所有相对于该坐标系匀速运动的坐标系中也有效。当然，我们的例子非常简单，即直线运动，其中坐标系可以用一根刚性杆来表示。但我们的结论一般都是有效的，可以总结如下：（1）我们不知道寻找惯性系的规则。

Newton’s law connecting the force with the change of velocity will, therefore, be valid in both C.S. Once again we reach a conclusion which is confirmed by everyday experience: if the laws of mechanics are valid in one C.S., then they are valid in all C.S. moving uniformly with respect to that one. O ur example was, of course, a very simple one, that o f rectilinear motion in which the C.S. can be represented by a rigid rod. But our conclusions are generally valid, and can be summarized as follows: (1) We know of no rule for finding an inertial system.

然而，给定一个，我们就能找到无数个，因为所有相对于彼此均匀运动的 CS 都是惯性系统，如果其中一个是惯性系统的话。

Given one, however, we can find an infinite number, since all C.S. moving uniformly, relative to each other, are inertial systems if one of them is.

(2) 同一事件所对应的时间在所有坐标系中都是相同的，但坐标和速度各有不同，并按照变换规律而变化。

(2) The time corresponding to an event is the same in all C.S. But the co-ordinates and velocities are different, and change according to the transformation laws.

（3）虽然从一个坐标系转换到另一个坐标系时，坐标和速度会发生变化，但是力和速度的变化，以及力学定律对于变换定律却是不变的。

(3) Although the co-ordinates and velocity change when passing from one C.S. to another, the force and change o f velocity, and therefore the laws of mechanics are invariant with respect to the transformation laws.

这里为坐标和速度制定的变换定律，我们称之为经典力学的变换定律，或简称为经典变换。

The laws o f transformation formulated here for coordinates and velocities we shall call the transformation laws of classical mechanics, or more briefly, the classical transformation.

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以太和移动

E T H E R A N D M O T IO N

伽利略相对论原理适用于机械现象。相同的力学定律适用于所有相对运动的惯性系统。这一原理是否也适用于非机械现象，尤其是那些场概念非常重要的现象？围绕这个问题的所有问题立即将我们带到了相对论的起点。

The Galilean relativity principle is valid for mechanical phenomena. The same laws o f mechanics apply to all inertial systems moving relative to each other. Is this principle also valid for non-mechanical phenomena, especially for those for which the field concepts proved so very important? A ll problems concentrated around this question immediately bring us to the starting-point o f the relativity theory.

我们记得，真空中（换句话说，以太中）的光速为每秒 186,000 英里，光是一种通过以太传播的电磁波。电磁场携带的能量一旦从其源头发射出来，就会独立存在。目前，我们将继续相信以太是一种传播电磁波（因此也是光波）的介质，尽管我们充分意识到与其机械结构相关的许多困难。

We remember that the velocity o f light in vacuo, or in other words, in ether, is 186,000 miles per second and that light is an electromagnetic wave spreading through the ether. The electromagnetic field carries energy which, once emitted from its source, leads an independent existence. For the time being, we shall continue to believe that the ether is a medium through which electromagnetic waves, and thus also light waves, are propagated, even though we are fully aware o f the many difficulties connected with its mechanical structure.

我们坐在一个封闭的房间里，与外界隔绝，空气无法进入或逸出。如果我们坐着不动并说话，从物理角度来看，我们就是在创造声波，这些声波从静止的声源以空气中的声音速度传播开来。如果嘴和耳朵之间没有空气或其他物质介质，我们就听不到声音。实验表明，如果没有风，并且空气在所选的 CS 中处于静止状态，则空气中的声音速度在所有方向上都是相同的。

We are sitting in a closed room so isolated from the external world that no air can enter or escape. I f we sit still and talk we are, from the physical point o f view, creating sound waves, which spread from their resting source with the velocity of sound in air. I f there were no air or other material medium between the mouth and the ear, we could not detect a sound. Experiment has shown that the velocity o f sound in air is the same in all directions, if there is no wind and the air is at rest in the chosen C.S.

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现在让我们想象一下我们的房间在空间中均匀移动。外面的人透过移动房间（或者如果你愿意的话，火车）的玻璃墙，看到里面发生的一切。从内部观察者的测量结果中，他可以推断出相对于他与周围环境相关的 CS 的声音速度，房间是相对于该 CS 移动的。这又是一个古老的、讨论过很多次的问题，即如果已经知道另一个 CS 中的速度，则确定一个 CS 中的速度。

Let us now imagine that our room moves uniformly through space. A man outside sees, through the glass walls of the moving room (or train if you prefer), everything which is going on inside. From the measurements of the inside observer he can deduce the velocity of sound relative to his C.S. connected with his surroundings, relative to which the room moves. Here again is the old, much discussed, problem of determining the velocity in one C.S. if it is already known in another.

房间里的观察者声称：对我来说，声音的速度在所有方向上都是相同的。

The observer in the room claims: the velocity of sound is, for me, the same in all directions.

外部观察者声称：声音在移动的房间中传播的速度在我的坐标系中是确定的，但在各个方向上的速度并不相同。它在房间运动的方向上大于标准声速，在相反的方向上则较小。

The outside observer claims: the velocity o f sound, spreading in the moving room and determined in my C.S., is not the same in all directions. It is greater than the standard velocity o f sound in the direction o f the motion of the room and smaller in the opposite direction.

这些结论是从经典变换中得出的，可以通过实验得到证实。房间内有物质介质，即声波传播的空气，因此，对于室内和室外的观察者来说，声音的速度会有所不同。

These conclusions are drawn from the classical transformation and can be confirmed by experiment. The room carries within it the material medium, the air through which sound waves are propagated, and the velocities of sound will, therefore, be different for the inside and outside observer.

我们可以从声音作为通过物质介质传播的波的理论中得出一些进一步的结论。听不见别人说话的一种方式（虽然这绝不是最简单的方式）是，以大于声音相对于说话者周围空气的速度奔跑。这样产生的声波就永远无法到达我们的耳朵。

We can draw some further conclusions from the theory of sound as a wave propagated through a material medium. One way, though by no means the simplest, of not hearing what someone is saying, is to run, with a velocity greater than that of sound, relative to the air surrounding the speaker. The sound waves produced will then never be able to reach our

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耳朵。另一方面，如果我们错过了一个永远不会重复的重要单词，我们必须以高于声音的速度奔跑才能到达产生的波并捕捉到单词。这两个例子都没有什么不合理之处，只是在这两种情况下，我们都必须以每秒大约四百码的速度奔跑，我们完全可以想象，进一步的技术发展将使这样的速度成为可能。从枪中射出的子弹实际上以高于声音的速度移动，而一个被子弹击中的人永远不会听到枪声。

ears. O n the other hand, if we missed an important word which will never be repeated, we must run with a speed greater than that of sound to reach the produced wave and to catch the word. There is nothing irrational in either of these examples except that in both cases we should have to run with a speed of about four hundred yards per second, and we can very well imagine that further technical development will make such speeds possible. A bullet fired from a gun actually moves with a speed greater than that of sound and a man placed on such a bullet would never hear the sound of the shot.

所有这些例子都具有纯机械性质，我们现在可以提出重要的问题：在光波的情况下，我们能重复刚才对声波所说的吗？伽利略相对论原理和经典变换是否适用于光学和电学现象以及机械现象？如果不深入探究这些问题的含义，就简单地用“是”或“否”来回答这些问题是危险的。

A ll these examples are of a purely mechanical character and we can now formulate the important questions: could we repeat what has just been said o f a sound wave, in the case of a light wave? Do the Galilean relativity principle and the classical transformation apply to optical and electrical phenomena as well as to mechanical? It would be risky to answer these questions by a simple “ yes” or “ n o ” without going more deeply into their meaning.

对于房间内声波相对于外部观察者均匀运动的情况，以下中间步骤对于我们得出结论非常重要：移动的房间内带有声波传播的空气。

In the case of the sound wave in the room moving uniformly, relative to the outside observer, the following intermediate steps are very essential for our conclusion: T he moving room carries the air in which the sound wave is propagated.

在两个相对于彼此匀速运动的坐标系中观察到的速度通过经典变换联系起来。

The velocities observed in two C.S. moving uniformly, relative to each other, are connected by the classical transformation.

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光的相应问题必须用稍微不同的方式表述。房间里的观察者不再说话，而是向各个方向发送光信号或光波。让我们进一步假设发射光信号的光源永久地静止在房间里。光波在以太中移动，就像声波在空气中移动一样。

The corresponding problem for light must be formulated a little differently. The observers in the room are no longer talking, but are sending light signals, or light waves in every direction. Let us further assume that the sources emitting the light signals are permanently resting in the room. The light waves move through the ether just as the sound waves moved through the air.

以太是否像空气一样随房间流动？

Is the ether carried with the room as the air was?

由于我们没有以太的机械图像，因此回答这个问题极其困难。如果房间是封闭的，里面的空气就会被迫随之移动。显然，以这种方式思考以太是没有意义的，因为所有物质都浸没在其中，而以太渗透到任何地方。没有一扇门对以太是关闭的。现在的“移动房间”仅指光源与之刚性连接的移动 CS。然而，我们可以想象，房间与其光源一起移动，以太也随之移动，就像声源和空气在封闭的房间中一起移动一样。但我们也可以想象相反的情况：房间在以太中移动，就像船在完全平静的海面上移动一样，不携带任何介质部分，而是在其中移动。在我们的第一幅图中，房间与其光源一起移动，以太随之移动。可以将其与声波进行类比，并得出非常相似的结论。

Since we have no mechanical picture of the ether, it is extremely difficult to answer this question. I f the room is closed, the air inside is forced to move with it. There is obviously no sense in thinking of ether in this way, since all matter is immersed in it and it penetrates everywhere. No doors are closed to ether. The ‘‘ moving room ” now means only a moving C.S. to which the source o f light is rigidly connected. It is, however, not beyond us to imagine that the room moving with its light source carries the ether along with it just as the sound source and air were carried along in the closed room. But we can equally well imagine the opposite: that the room travels through the ether as a ship through a perfectly smooth sea, not carrying any part o f the medium along but moving through it. In our first picture, the room moving with its light source carries the ether. A n analogy with a sound wave is possible and quite similar conclusions can be drawn.

在第二种情况下，随着光源移动的房间不携带以太。与声波没有任何相似之处，因此本案例中得出的结论

In the second, the room moving with its light source does not carry the ether. No analogy with a sound wave is possible and the conclusions drawn in the case

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声波的极限不适用于光波。这是两种极限可能性。我们可以想象一种更复杂的可能性，即以太仅部分地由随光源移动的房间携带。但在找出实验支持的两个更简单的极限情况中的哪一个之前，没有理由讨论更复杂的假设。

o f a sound wave do not hold for a light wave. These are the two limiting possibilities. We could imagine the still more complicated possibility that the ether is only partially carried by the room moving with its light source. But there is no reason to discuss the more complicated assumptions before finding out which o f the two simpler limiting cases experiment favours.

我们从第一幅图开始，现在假设：以太由与其刚性连接的光源一起移动的房间携带。如果我们相信声波速度的简单变换原理，我们现在也可以将我们的结论应用于光波。没有理由怀疑简单的机械变换定律，它只规定在某些情况下必须增加速度，在其他情况下必须减去速度。因此，目前，我们既假设以太由与其光源一起移动的房间携带，也假设经典变换。

We shall begin with our first picture and assume, for the present: the ether is carried along by the room moving with its rigidly connected light source. I f we believe in the simple transformation principle for the velocities o f sound waves, we can now apply our conclusions to light waves as well. There is no reason for doubting the simple mechanical transformation law which only states that the velocities have to be added in certain cases and subtracted in others. For the moment, therefore, we shall assume both the carrying o f the ether by the room moving with its light source and the classical transformation.

如果我打开灯，并且其光源与我的房间牢固连接，那么光信号的速度就是众所周知的实验值 186,000

I f I turn on the light and its source is rigidly connected with my room, then the velocity o f the light signal has the well-known experimental value 186,000

英里每秒。但是外部观察者会注意到房间的运动，因此也会注意到光源的运动——而且，由于以太被带走，他的结论一定是：我的外部坐标系中的光速

miles per second. But the outside observer will notice the motion of the room, and, therefore, that of the source— and, since the ether is carried along, his conclusion must be: the velocity of light in my outside C.S.

在不同方向上是不同的。在房间运动的方向上，它大于标准光速，在相反方向上则较小。

is different in different directions. It is greater than the standard velocity of light in the direction of the motion of the room and smaller in the opposite direction.

我们的结论是：如果乙醚随房间流动

O ur conclusion is: if ether is carried with the room

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物体随光源一起移动，如果力学定律成立，那么光速就必须取决于光源的速度。如果光源朝我们运动，那么从移动光源到达我们眼睛的光速会更大，如果光源远离我们，那么光速会更小。

moving with its light source and if the mechanical laws are valid, then the velocity of light must depend on the velocity of the light source. Light reaching our eyes from a moving light source would have a greater velocity if the motion is toward us and smaller if it is away from us.

如果我们的速度大于光速，我们就能够逃离光信号。我们可以通过接触之前发出的光波来看到过去发生的事情。我们应该以与发送顺序相反的顺序捕捉它们，地球上发生的事情序列就会像倒放的电影一样出现，以一个美好的结局开始。

I f our speed were greater than that o f light, we should be able to run away from a light signal. We could see occurrences from the past by reaching previously sent light waves. We should catch them in a reverse order to that in which they were sent, and the train of happenings on our earth would appear like a film shown backward, beginning with a happy ending.

这些结论都是基于运动的坐标系携带以太且机械变换定律成立的假设。如果是这样，光和声音之间的类比就是完美的。

These conclusions all follow from the assumption that the moving C.S. carries along the ether and the mechanical transformation laws are valid. I f this is so, the analogy between light and sound is perfect.

但没有任何迹象表明这些结论的真实性。相反，它们与所有旨在证明这些结论的观察结果相矛盾。尽管这一结论是通过间接实验得出的，但考虑到光速的巨大值所造成的巨大技术困难，这一结论的清晰度毫无疑问。 光速在所有 CS中始终相同

But there is no indication as to the truth o f these conclusions. O n the contrary, they are contradicted by all observations made with the intention o f proving them. There is not the slightest doubt as to the clarity o f this verdict, although it is obtained through rather indirect experiments in view of the great technical difficulties caused by the enormous value of the velocity of light. The velocity o f light is always the same in all C.S.

无论发射源是否移动， 或如何 移动。

independent o f whether or not the emitting source moves, or how it moves.

我们不会详细描述从中得出这一重要结论的许多实验。然而，我们可以使用一些非常简单的

We shall not go into detailed description of the many experiments from which this important conclusion can be drawn. We can, however, use some very simple

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尽管这些论据不能证明光速与源的运动无关，但却使这一事实令人信服和可以理解。

arguments which, though they do not prove that the velocity of light is independent o f the motion of the source, nevertheless make this fact convincing and understandable.

在我们的行星系统中，地球和其他行星围绕太阳旋转。我们不知道是否存在与我们类似的其他行星系统。然而，有很多双星系统，由两颗恒星围绕一个点移动，这个点称为它们的重心。对这些双星运动的观察揭示了牛顿引力定律的有效性。

In our planetary system the earth and other planets move around the sun. We do not know of the existence o f other planetary systems similar to ours. There are, however, very many double-star systems, consisting of two stars moving around a point, called their centre of gravity. Observation of the motion of these double stars reveals the validity of Newton’s gravitational law.

现在假设光速取决于发射体的速度。那么信息，即来自恒星的光线，将根据光线发射时恒星的速度而传播得更快或更慢。在这种情况下，整个运动就会变得混乱，在遥远的双星情况下，不可能证实统治我们行星系统的引力定律的有效性。

Now suppose that the speed of light depends on the velocity of the emitting body. Then the message, that is, the light ray from the star, will travel more quickly or more slowly, according to the velocity o f the star at the moment the ray is emitted. In this case the whole motion would be muddled and it would be impossible to confirm, in the case of distant double stars, the validity of the same gravitational law which rules over our planetary system.

让我们考虑另一个基于非常简单的想法的实验。想象一个轮子快速旋转。

Let us consider another experiment based upon a very simple idea. Imagine a wheel rotating very quickly.

根据我们的假设，以太被运动所携带并参与其中。当车轮静止时，光波在车轮附近通过时的速度与车轮运动时的速度不同。静止以太中的光速应该与被车轮运动快速拖曳的以太中的光速不同，就像声波的速度在平静和有风的日子里会发生变化一样。但事实并非如此

According to our assumption, the ether is carried by the motion and takes a part in it. A light wave passing near the wheel would have a different speed when the wheel is at rest than when it is in motion. The velocity of light in ether at rest should differ from that in ether which is being quickly dragged round by the motion o f the wheel, just as the velocity of a sound wave varies on calm and windy days. But no such

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发现差异！无论我们从哪个角度来探讨这个问题，或者我们设计什么关键实验，结论总是与运动携带以太的假设相反。因此，我们的考虑结果，在更详细和技术论证的支持下，是：

difference is detected! No matter from which angle we approach the subject, or what crucial experiment we may devise, the verdict is always against the assumption of the ether carried by motion. Thus, the result of our considerations, supported by more detailed and technical argument, is:

光速与发射源的运动无关。

The velocity o f light does not depend on the motion of the emitting source.

不能假设运动的物体会带着周围的以太一起运动。

It must not be assumed that the moving body carries the surrounding ether along.

因此，我们必须放弃声波与光波之间的类比，转而考虑第二种可能性：所有物质都通过以太运动，而以太根本不参与运动。这意味着我们假设存在一个以太之海，其中所有 CS

We must, therefore, give up the analogy between sound and light waves and turn to the second possibility: that all matter moves through the ether, which takes no part whatever in the motion. This means that we assume the existence o f a sea o f ether with all C.S.

静止于其中，或相对于它运动。假设我们暂时不去思考实验是否证实或反驳了这一理论。最好更熟悉这一新假设的含义以及可以从中得出的结论。

resting in it, or moving relative to it. Suppose we leave, for a while, the question as to whether experiment proved or disproved this theory. It will be better to become more familiar with the meaning of this new assumption and with the conclusions which can be drawn from it.

存在一个相对于以太海静止的坐标系。

There exists a C.S. resting relative to the ether-sea.

在力学中，众多相对于彼此匀速运动的坐标系中没有一个是能够被区分的。

In mechanics, not one o f the many C.S. moving uniformly, relative to each other, could be distinguished.

所有这些坐标系都同样“好”或“坏”。如果我们有两个坐标系相对匀速运动，那么在力学中，问它们中哪一个在运动，哪一个在静止是没有意义的。只能观察到相对匀速运动。由于伽利略相对论，我们无法谈论绝对匀速运动

A ll such C.S. were equally “ good” or “ b a d ” . I f we have two C.S. moving uniformly, relative to each other, it is meaningless, in mechanics, to ask which o f them is in motion and which at rest. O n ly relative uniform motion can be observed. We cannot talk about absolute uniform motion because of the Galilean relativity

[8度

[8o

原理。绝对匀速运动而不仅仅是相对匀速运动这一说法是什么意思呢？简单地说，存在一个坐标系，其中某些自然定律与其他坐标系中的不同。此外，每个观察者都可以通过比较该坐标系中有效的定律与唯一一个具有绝对垄断权作为标准坐标系的坐标系中有效的定律来检测其坐标系是静止还是运动。这与经典力学的情况不同，在经典力学中，由于伽利略的惯性定律，绝对匀速运动毫无意义。

principle. What is meant by the statement that absolute and not only relative uniform motion exists? Simply that there exists one C.S. in which some of the laws of nature are different from those in all others. Also that every observer can detect whether his C.S. is at rest or in motion by comparing the laws valid in it with those valid in the only one which has the absolute monopoly of serving as the standard C.S. Here is a different state of affairs from classical mechanics, where absolute uniform motion is quite meaningless because of Galileo’s law of inertia.

如果假设通过以太运动，那么在场现象领域可以得出什么结论？

What conclusions can be drawn in the domain of field phenomena if motion through ether is assumed?

这意味着存在一个不同于所有其他坐标系的坐标系，相对于以太海处于静止状态。很明显，在这个坐标系中，一些自然定律一定有所不同，否则“通过以太的运动”这一短语就毫无意义了。如果伽利略相对论原理有效，那么通过以太的运动就毫无意义。这两种观点是无法调和的。

This would mean that there exists one C.S. distinct from all others, at rest relative to the ether-sea. It is quite clear that some o f the laws o f nature must be different in this C.S., otherwise the phrase “ motion through ether” would be meaningless. I f the Galilean relativity principle is valid, then motion through ether makes no sense at all. It is impossible to reconcile these two ideas.

然而，如果存在一个由以太固定的特殊坐标系，那么谈论“绝对运动”或“绝对静止”就有了确定的意义。

If, however, there exists one special C.S. fixed by the ether, then to speak of “ absolute motion” or “ absolute rest” has a definite meaning.

我们真的别无选择。我们试图通过假设系统在运动时会带动以太来挽救伽利略相对论，但这与实验相矛盾。唯一的出路是放弃伽利略相对论，尝试假设所有物体都在平静的以太海中运动。

We really have no choice. We tried to save the Galilean relativity principle by assuming that systems carry the ether along in their motion, but this led to a contradiction with experiment. The only way out is to abandon the Galilean relativity principle and try out the assumption that all bodies move through the calm ether-sea.

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下一步是考虑一些与伽利略相对论原理相矛盾、支持以太运动观点的结论，并进行实验检验。这样的实验很容易想象，但很难进行。由于我们这里只关心想法，所以我们不必担心技术难题。

The next step is to consider some conclusions contradicting the Galilean relativity principle and supporting the view of motion through ether, and to put them to the test of an experiment. Such experiments are easy enough to imagine, but very difficult to perform. As we are concerned here only with ideas, we need not bother with technical difficulties.

我们再次回到移动的房间，里面有两个观察者，一个在里面，一个在外面。外面的观察者将代表标准坐标系，以太海为代表。这是光速始终具有相同标准值的杰出坐标系。

Again we return to our moving room with two observers, one inside and one outside. The outside observer will represent the standard C.S., designated by the ether-sea. It is the distinguished C.S. in which the velocity of light always has the same standard value.

所有光源，无论是移动的还是静止在平静的以太海中的，都以相同的速度传播光。

A ll light sources, whether moving or at rest in the calm ether-sea, propagate light with the same velocity.

房间和其中的观察者在以太中移动。

The room and its observer move through the ether.

设想房间中央有一盏灯忽明忽暗，而且房间的墙壁是透明的，这样里外的观察者都可以测量光速。如果我们问这两个观察者他们期望得到什么结果，他们的回答会大致如下：外面的观察者： 我的坐标系由以太海指定。在我的坐标系中，光始终具有标准值。我不需要关心光源或其他物体是否在运动，因为它们从不带着我的以太海移动。我的坐标系与所有其他坐标系都不同，光速在这个坐标系中必定有其标准值，与光束的方向或光源的运动无关。

Imagine that a light in the centre o f the room is flashed on and off and, furthermore, that the walls of the room are transparent so that the observers, both inside and outside, can measure the velocity o f the light. I f we ask the two observers what results they expect to obtain, their answers would run something like this: The outside observer: M y C.S. is designated by the ether-sea. Light in my C.S. always has the standard value. I need not care whether or not the source of light or other bodies are moving, for they never carry my ether-sea with them. M y C.S. is distinguished from all others and the velocity o f light must have its standard value in this C.S., independent of the direction of the light beam or the motion of its source.

内部观察者： 我的房间穿过

The inside observer: M y room moves through the

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以太海。其中一面墙远离光，另一面墙靠近光。如果我的房间相对于以太海以光速运动，那么从房间中心发出的光就永远不会到达以光速运动的墙壁。如果房间的运动速度小于光速，那么从房间中心发出的波将先于另一面墙到达其中一面墙。向光波运动的墙壁将先于远离光波的墙壁到达。因此，尽管光源与我的 CS 刚性连接，但光速在所有方向上并不相同。当墙壁远离光时，它在相对于以太海的运动方向上会变小，而当墙壁向波运动并试图尽快与波相遇时，它在相反方向上会变大。

ether-sea. One of the walls runs away from the light and the other approaches it. I f my room travelled, relative to the ether-sea, with the velocity of light, then the light emitted from the centre of the room would never reach the wall running away with the velocity o f light. I f the room travelled with a velocity smaller than that of light, then a wave sent from the centre of the room would reach one of the walls before the other. The wall moving toward the light wave would be reached before the one retreating from the light wave. Therefore, although the source of light is rigidly connected with my C.S., the velocity of light will not be the same in all directions. It will be smaller in the direction of the motion relative to the ether-sea as the wall runs away, and greater in the opposite direction as the wall moves toward the wave and tries to meet it sooner.

因此，只有在以太海所区分的一个坐标系中，光速在所有方向上才应该是相等的。

Thus, only in the one C.S. distinguished by the ether-sea should the velocity of light be equal in all directions.

对于相对于以太海移动的其他 CS，它应该取决于我们测量的方向。

For other C.S. moving relatively to the ether-sea it should depend on the direction in which we are measuring.

刚刚考虑的关键实验使我们能够检验穿越以太海的运动理论。

The crucial experiment just considered enables us to test the theory of motion through the ether-sea.

事实上，大自然为我们提供了一个以相当高的速度运动的系统——地球绕太阳旋转一年。如果我们的假设是正确的，那么地球运动方向上的光速应该与相反方向上的光速不同。这些差异可以计算出来

Nature, in fact, places at our disposal a system moving with a fairly high velocity— the earth in its yearly motion around the sun. I f our assumption is correct, then the velocity of light in the direction o f the motion of the earth should differ from the velocity of light in an opposite direction. The differences can be calculated

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并设计了合适的实验测试。考虑到理论得出的时间差很小，必须想出非常巧妙的实验安排。著名的迈克尔逊-莫雷实验就是这样做的。结果是“死亡”的判决

and a suitable experimental test devised. In view of the small time-differences following from the theory, very ingenious experimental arrangements have to be thought out. This was done in the famous Michelson-Morley experiment. The result was a verdict of “ death”

平静的以太海理论，所有物质都通过以太海运动。没有发现光速与方向的依赖关系。如果以太海理论被假设，那么不仅光速，而且其他场现象也会显示出对运动 CS 方向的依赖性。每个实验都给出了与迈克尔逊-莫雷实验相同的负面结果，并且从未揭示出对地球运动方向的任何依赖性。

to the theory o f a calm ether-sea through which all matter moves. No dependence of the speed of light upon direction could be found. Not only the speed of light, but also other field phenomena would show a dependence on the direction in the moving C.S., if the theory of the ether-sea were assumed. Every experiment has given the same negative result as the Michelson-Morley one, and never revealed any dependence upon the direction of the motion of the earth.

情况变得越来越严重。人们尝试了两种假设。第一，运动物体携带以太。光速不依赖于光源运动的事实与这一假设相矛盾。第二，存在一个独特的坐标系，运动物体不携带以太，而是穿过一个永远平静的以太海。如果是这样，那么伽利略相对论原理就不成立，光速不可能在每个坐标系中都相同。我们再次与实验相矛盾。

The situation grows more and more serious. Two assumptions have been tried. The first, that moving bodies carry ether along. The fact that the velocity of light does not depend on the motion of the source contradicts this assumption. The second, that there exists one distinguished C.S. and that moving bodies do not carry the ether but travel through an ever calm ether-sea. I f this is so, then the Galilean relativity principle is not valid and the speed of light cannot be the same in every C.S. Again we are in contradiction with experiment.

人们尝试了更多的人为理论，假设真正的事实介于这两种极限情况之间：以太只是部分地被运动的物体携带。但他们都失败了！所有试图解释电磁现象的尝试

More artificial theories have been tried out, assuming that the real truth lies somewhere between these two limiting cases: that the ether is only partially carried by the moving bodies. But they all failed ! Every attempt to explain the electromagnetic phenomena in

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借助以太运动、通过以太运动、或者这两种运动来移动 CS 都被证明是不成功的。

moving C.S. with the help of the motion of the ether, motion through the ether, or both these motions, proved unsuccessful.

于是，科学史上最戏剧性的一幕出现了。所有关于以太的假设都毫无结果！实验结论总是否定的。回顾物理学的发展，我们看到，以太在诞生后不久就成为物理实体家族中可怕的孩子 。首先，构造以太的简单机械图像被证明是不可能的，因此被抛弃了。这在很大程度上导致了机械观点的崩溃。其次，我们不得不放弃希望，即通过以太海的存在，一个CS将被区分出来，并导致对绝对运动而不仅仅是相对运动的认识。

Thus arose one of the most dramatic situations in the history of science. A ll assumptions concerning ether led nowhere! The experimental verdict was always negative. Looking back over the development of physics we see that the ether, soon after its birth, became the enfant terrible of the family of physical substances. First, the construction of a simple mechanical picture of the ether proved to be impossible and was discarded. This caused, to a great extent, the breakdown of the mechanical point of view. Second, we had to give up hope that through the presence of the ether-sea one C.S. would be distinguished and lead to the recognition o f absolute, and not only relative, motion.

除了传送波以外，这应该是以太能够标记和证明其存在的唯一方法。我们让以太真实存在的所有尝试都失败了。

This would have been the only way, besides carrying the waves, in which ether could mark and justify its existence. A ll our attempts to make ether real failed.

它既没有揭示以太的机械结构，也没有揭示绝对运动。以太的所有属性除了它被发明出来的原因，即它传输电磁波的能力之外，什么也没有留下。我们试图发现以太的属性，却遇到了困难和矛盾。在经历了如此糟糕的经历后，现在是彻底忘记以太并永远不要提及它的名字的时候了。我们应该说：我们的空间具有传输波的物理属性，这样就不用使用我们决定避免使用的词了。

It revealed neither its mechanical construction nor absolute motion. Nothing remained of all the properties of the ether except that for which it was invented, i.e. its ability to transmit electromagnetic waves. O ur attempts to discover the properties of the ether led to difficulties and contradictions. After such bad experiences, this is the moment to forget the ether completely and to try never to mention its name. We shall say: our space has the physical property o f transmitting waves, and so omit the use of a word we have decided to avoid.

从我们的词汇中省略一个词意味着

The omission o f a word from our vocabulary is, of

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当然，没有补救办法。我们的 1

course, no remedy. O ur t 1

卢布确实太

roubles are indeed much too

用这种方法可以解决深刻的问题！

profound to be solved in this w a y !

现在让我们把那些已经得到实验充分证实的事实写下来，而不再关心“e—

Let us now write down the facts which have been sufficiently confirmed by experiment without bothering any more about the “ e—

r”问题。

r ” problem.

（1）光在空空间中的传播速度总有它的标准值，与光源或光接收器的运动无关。

(1) The velocity o f light in empty space always has its standard value, independent of the motion of the source or receiver of light.

（2）在两个相对匀速运动的坐标系中，一切自然定律都是完全相同的，无法区分绝对匀速运动。

(2) In two C.S. moving uniformly, relative to each other, all laws of nature are exactly identical and there is no way of distinguishing absolute uniform motion.

有许多实验证实了这两个陈述，没有一个与它们中的任何一个相矛盾。第一个陈述表达了光速的恒定特性，第二个陈述将针对机械现象制定的伽利略相对论原理推广到自然界的所有事件。

There are many experiments to confirm these two statements and not a single one to contradict either of them. The first statement expresses the constant character of the velocity of light, the second generalizes the Galilean relativity principle, formulated for mechanical phenomena, to all happenings in nature.

在力学中，我们已经看到：如果一个质点的速度相对于一个坐标系是这样的，那么相对于第一个坐标系，在另一个匀速运动的坐标系中，它的速度就会有所不同。这是从简单的机械变换原理得出的。这些原理是由我们的直觉（人相对于船和岸边运动）直接给出的，显然这里不会有什么问题！但这个变换定律与光速的恒定性相矛盾。或者，换句话说，我们增加了第三个原理：

In mechanics, we have seen: I f the velocity o f a material point is so and so, relative to one C.S., then it will be different in another C.S. moving uniformly, relative to the first. This follows from the simple mechanical transformation principles. They are immediately given by our intuition (man moving relative to ship and shore) and apparently nothing can be wrong here ! But this transformation law is in contradiction to the constant character of the velocity of light. O r, in other words, we add a third principle:

（3）位置和速度按照经典变换从一个惯性系变换到另一个惯性系。

(3) Positions and velocities are transformed from one inertial system to another according to the classical transformation.

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矛盾显而易见。我们不能把（i）、（2）和（3）结合起来。

The contradiction is then evident. We cannot combine (i), (2), and (3).

经典变换似乎太明显、太简单了，以至于任何试图改变它的尝试都无法实现。我们已经尝试过改变（1）和（2），但与实验结果不一致。所有关于“电子”运动的理论——

The classical transformation seems too obvious and simple for any attempt to change it. We have already tried to change (1) and (2) and came to a disagreement with experiment. A ll theories concerning the motion of “ e—

r”要求对（1）进行修改，并且

r ” required an alteration of (1) and

（2）。这没有用。我们再一次意识到我们困难的严重性。需要一条新的线索。这条线索是通过 接受基本假设 （1）和（2）并放弃（3）来提供的，尽管这看起来很奇怪。新的线索从对最基本和最原始的概念的分析开始；我们将展示这种分析如何迫使我们改变旧观点并消除所有困难。

(2). This was no good. Once more we realize the serious character of our difficulties. A new clue is needed. It is supplied by accepting the fundamental assumptions (1) and (2), and, strange though it seems, giving up (3). The new clue starts from an analysis of the most fundamental and primitive concepts; we shall show how this analysis forces us to change our old views and removes all our difficulties.

时间、距离、相对论

T IM E , D IS T A N C E , R E L A T I V I T Y

我们的新假设是：

O ur new assumptions are:

（1）真空中 的光速在所有坐标系中都是相同的

(1) The velocity o f light in vacuo is the same in all C.S.

相对彼此均匀运动.

moving uniformly, relative to each other.

（2） 一切自然定律，在所有相对彼此匀速运动的坐标系中都是相同的。

(2) A ll laws of nature are the same in all C.S. moving uniformly, relative to each other.

相对论就是从这两个假设开始的。从现在起，我们将不再使用经典变换，因为我们知道它与我们的假设相矛盾。

The relativity theory begins with these two assumptions. From now on we shall not use the classical transformation because we know that it contradicts our assumptions.

就像科学界一贯的做法一样，我们在这里必须摆脱根深蒂固的、经常不加批判地重复的偏见。既然我们已经看到，（1）和（2）的变化会导致与实验相矛盾，那么我们必须

It is essential here, as always in science, to rid ourselves o f deep-rooted, often uncritically repeated, prejudices. Since we have seen that changes in (1) and (2) lead to contradiction with experiment, we must have

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勇于清楚地陈述它们的有效性，并攻击一个可能的弱点，即位置和速度从一个 CS 转换到另一个 CS 的方式。

the courage to state their validity clearly and to attack the one possibly weak point, the way in which positions and velocities are transformed from one C.S. to another.

我们的目的是从 (1) 和 (2) 中得出结论，看看这些假设在何处以及如何与经典变换相矛盾，并找到所获结果的物理意义。

It is our intention to draw conclusions from (1) and (2), see where and how these assumptions contradict the classical transformation, and find the physical meaning o f the results obtained.

再次使用移动房间的例子，房间内和外部都有观察者。再次从房间中心发出光信号，我们再次询问这两个人他们期望观察到什么，只假设我们的两个原理，忘记之前关于光传播介质的说法。我们引用他们的答案：内部观察者： 从房间中心传播的光信号将同时到达墙壁，因为所有墙壁与光源的距离都相等，并且光速在所有方向上都相同。

Once more, the example o f the moving room with outside and inside observers will be used. Again a light signal is emitted from the centre of the room and again we ask the two men what they expect to observe, assuming only our two principles and forgetting what was previously said concerning the medium through which the light travels. We quote their answers: The inside observer: The light signal travelling from the centre o f the room will reach the walls simultaneously, since all the walls are equally distant from the light source and the velocity o f light is the same in all directions.

外部观察者： 在我的系统中，光速与随房间移动的观察者的速度完全相同。光源在我的 CS 中是否移动对我来说并不重要，因为它的运动不会影响光速。我看到的是光信号以标准速度传播，在所有方向上都相同。其中一堵墙正试图逃离光信号，而另一堵墙正试图接近光信号。

The outside observer: In my system, the velocity of light is exactly the same as in that o f the observer moving with the room. It does not matter to me whether or not the light source moves in my C.S. since its motion does not influence the velocity of light. What I see is a light signal travelling with a standard speed, the same in all directions. O ne o f the walls is trying to escape from and the opposite wall to approach the light signal.

因此，逃逸墙会比接近墙接收到信号稍晚一些。虽然如果房间速度

Therefore, the escaping wall will be met by the signal a little later than the approaching one. Although the difference will be very slight if the velocity of the room

与 1 相比较小

is small compared with th 1

光，光信号

at of light, the light signal

然而，不会同时与这两个垂直于运动方向的相对墙壁相遇。

will nevertheless not meet these two opposite walls, which are perpendicular to the direction o f the motion, quite simultaneously.

比较两个观察者的预测，我们发现了一个最令人吃惊的结果，它与经典物理学看似有理有据的概念截然相反。两个事件，即到达两面墙的两束光束，对于内部的观察者来说是同时发生的，但对于外部的观察者来说却不是。在经典物理学中，对于所有 CS Time 中的所有观察者，我们都有一个时钟、一个时间流，因此“同时”、“更早”、“更晚”等词具有独立于任何 CS 的绝对含义。在一个 CS 中同时发生的两个事件必然在所有其他 CS 中同时发生

Comparing the predictions of our two observers, we find a most astonishing result which flatly contradicts the apparently well-founded concepts o f classical physics. Two events, i.e., the two light beams reaching the two walls, are simultaneous for the observer on the inside, but not for the observer on the outside. In classical physics, we had one clock, one time flow, for all observers in all C.S. Tim e, and therefore such words as “ simultaneously” , “ sooner” , “ later” , had an absolute meaning independent o f any C.S. Two events happening at the same time in one C.S. happened necessarily simultaneously in all other C.S.

假设 (1) 和 (2)，即相对论，迫使我们放弃这种观点。我们描述了在一个 CS 中同时发生的两个事件，但在另一个 CS 中发生在不同的时间。我们的任务是理解这个结果，理解这句话的含义：“在一个 CS 中同时发生的两个事件，在另一个 CS 中可能不是同时发生的”

Assumptions (1) and (2), i.e. the relativity theory, force us to give up this view. We have described two events happening at the same time in one C.S., but at different times in another C.S. O ur task is to understand this consequence, to understand the meaning o f the sentence: “ Two events which are simultaneous in one C.S., may not be simultaneous in another C.S.”

“一个 CS 中同时发生的两个事件”是什么意思？直觉上，每个人似乎都知道这句话的意思。但让我们下定决心谨慎行事，并尝试给出严格的定义，因为我们知道高估直觉是多么危险。

W hat do we mean by “ two simultaneous events in one C.S.” ? Intuitively everyone seems to know the meaning o f this sentence. But let us make up our minds to be cautious and try to give rigorous definitions, as we know how dangerous it is to over-estimate intuition.

我们先来回答一个简单的问题。

Let us first answer a simple question.

什么是时钟？

What is a clock?

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对时间流动的原始主观感觉使我们能够整理印象，判断一个事件发生得早，另一个事件发生得晚。但是为了显示两个事件之间的时间间隔是 10 秒，就需要一个时钟。通过使用时钟，时间概念变得客观。任何物理现象都可以用作时钟，只要它能根据需要精确重复多次。将此类事件开始和结束之间的间隔作为一个时间单位，可以通过重复这一物理过程来测量任意时间间隔。所有的时钟，从简单的沙漏到最精密的仪器，都是基于这个想法的。沙漏的时间单位是沙子从上层沙漏流到下层沙漏所需的间隔。通过倒置沙漏可以重复相同的物理过程。

The primitive subjective feeling of time flow enables us to order our impressions, to judge that one event takes place earlier, another later. But to show that the time interval between two events is 10 seconds, a clock is needed. By the use o f a clock the time concept becomes objective. A ny physical phenomenon may be used as a clock, provided it can be exactly repeated as many times as desired. Taking the interval between the beginning and the end o f such an event as one unit of time, arbitrary time intervals may be measured by repetition of this physical process. A ll clocks, from the simple hour-glass to the most refined instruments, are based on this idea. With the hour-glass the unit of time is the interval the sand takes to flow from the upper to the lower glass. The same physical process can be repeated by inverting the glass.

在两个相距很远的地方，我们有两个完美的时钟，它们显示的时间完全相同。无论我们多么仔细地验证，这个说法都应该是正确的。

A t two distant points we have two perfect clocks, showing exactly the same time. This statement should be true regardless of the care with which we verify it.

但这究竟意味着什么呢？我们如何才能确保相距遥远的时钟始终显示完全相同的时间？

But what does it really mean? How can we make sure that distant clocks always show exactly the same time?

一种可能的方法是使用电视。应该理解，电视只是作为一个例子，对我们的论证来说并不是必要的。我可以站在其中一个时钟旁边，看着另一个时钟的电视画面。然后我可以判断它们是否同时显示相同的时间。但这不是一个很好的证明。电视画面通过电磁波传输，因此以光速传播。通过电视，我

One possible method would be to use television. It should be understood that television is used only as an example and is not essential to our argument. I could stand near one of the clocks and look at a televised picture of the other. I could then judge whether or not they showed the same time simultaneously. But this would not be a good proof. The televised picture is transmitted through electromagnetic waves and thus travels with the speed o f light. Through television I

我看到的是不久前发送的图片，而在真实的时钟上，我看到的是当前正在发生的事情。这个困难很容易避免。我必须在距离两个时钟等远的一点拍摄电视照片，并从这个中心点观察它们。然后，如果信号同时发出，它们都会在同一时刻到达我。如果从它们之间距离的中点观察两个好的时钟总是显示相同的时间，那么它们非常适合指示两个远距离点事件的时间。

see a picture which was sent some very short time before, whereas on the real clock I see what is taking place at the present moment. This difficulty can easily be avoided. I must take television pictures of the two clocks at a point equally distant from each of them and observe them from this centre point. Then, if the signals are sent out simultaneously, they will all reach me at the same instant. I f two good clocks observed from the mid-point of the distance between them always show the same time, then they are well suited for designating the time of events at two distant points.

在机械学中，我们只使用一个时钟。但这不太方便，因为我们必须在这一个时钟附近进行所有测量。从远处看时钟，例如通过电视，我们总是要记住我们现在看到的事情实际上发生得更早，就像在观看日落时，我们在事件发生 8 分钟后才注意到它一样。

In mechanics we used only one clock. But this was not very convenient, because we had to take all measurements in the vicinity of this one clock. Looking at the clock from a distance, for example by television, we have always to remember that what we see now really happened earlier, just as in viewing the setting sun we note the event eight minutes after it has taken place.

我们应该根据我们与时钟的距离，对所有的时间读数进行修正。

We should have to make corrections, according to our distance from the clock, in all our time readings.

因此，只有一个时钟是很不方便的。

It is, therefore, inconvenient to have only one clock.

但是，既然我们知道如何判断两个或更多时钟是否同时显示相同的时间并以相同的方式运行，那么我们完全可以想象给定 CS 中任意数量的时钟。每个时钟都将帮助我们确定其附近发生的事件的时间。这些时钟相对于 CS 都处于静止状态。它们是“好”时钟并且是 同步的，这意味着它们同时显示相同的时间。

Now, however, as we know how to judge whether two, or more, clocks show the same time simultaneously and run in the same way, we can very well imagine as many clocks as we like in a given C.S. Each of them will help us to determine the time of the events happening in its immediate vicinity. The clocks are all at rest relative to the C.S. They are “ good” clocks and are synchronized, which means that they show the same time simultaneously.

没有什么特别的 1

There is nothing especiall 1

y 引人注目或奇怪

y striking or strange about

我们时钟的排列。我们现在使用许多同步时钟，而不是只有一个，因此，我们可以轻松判断两个遥远的事件在给定的 CS 中是否同时发生，如果它们附近的同步时钟在事件发生的瞬间显示相同的时间，它们就是同时发生的。说其中一个遥远的事件发生在另一个之前现在具有明确的含义。所有这些都可以借助我们 CS 中静止的同步时钟来判断

the arrangement of our clocks. We are now using many synchronized clocks instead of only one and can, therefore, easily judge whether or not two distant events are simultaneous in a given C.S. They are if the synchronized clocks in their vicinity show the same time at the instant the events happen. T o say that one of the distant events happens before the other has now a definite meaning. A ll this can be judged by the help of the synchronized clocks at rest in our C.S.

这与经典物理学是一致的，并且目前还没有出现任何与经典变换相矛盾的情况。

This is in agreement with classical physics, and not one contradiction to the classical transformation has yet appeared.

为了定义同时发生的事件，时钟通过信号同步。在我们的安排中，这些信号以光速传播是至关重要的，光速在相对论中起着至关重要的作用。

For the definition of simultaneous events, the clocks are synchronized by the help of signals. It is essential in our arrangement that these signals travel with the velocity of light, the velocity which plays such a fundamental role in the theory of relativity.

由于我们希望解决两个相对于彼此均匀运动的 CS 这一重要问题，我们必须考虑两根杆，每根杆都配有时钟。

Since we wish to deal with the important problem of two C.S. moving uniformly, relative to each other, we must consider two rods, each provided with clocks.

现在，两个相对运动的坐标系中的观察者各自都有自己的杆，杆上牢固地连接着一组时钟。

The observer in each of the two C.S. moving relative to each other now has his own rod with his own set of clocks rigidly attached.

在讨论经典力学中的测量时，我们为所有 CS 使用一个时钟。这里我们在每个 CS 中都使用多个时钟。这个差异并不重要。一个时钟就足够了，但没有人会反对使用多个时钟，只要它们表现得像同步时钟一样。

When discussing measurements in classical mechanics, we used one clock for all C.S. Here we have many clocks in each C.S. This difference is unimportant. One clock was sufficient, but nobody could object to the use o f many, so long as they behave as decent synchronized clocks should.

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现在，我们正接近经典变换与相对论相矛盾的关键点。当两组时钟相对均匀移动时会发生什么？古典物理学家会回答：什么也不会发生；它们仍然有相同的节奏，我们可以使用移动和静止的时钟来指示时间。根据经典物理学，在一个 CS 中同时发生的两个事件也将在任何其他 CS 中同时发生

Now we are approaching the essential point showing where the classical transformation contradicts the theory o f relativity. What happens when two sets of clocks are moving uniformly, relative to each other? The classical physicist would answer: Nothing; they still have the same rhythm, and we can use moving as well as resting clocks to indicate time. According to classical physics, two events simultaneous in one C.S. will also be simultaneous in any other C.S.

但这不是唯一可能的答案。我们同样可以想象一个运动的时钟与静止的时钟具有不同的节奏。现在让我们讨论这种可能性，暂时不决定时钟是否真的会在运动中改变其节奏。运动的时钟会改变其节奏的说法是什么意思？为了简单起见，我们假设在上 CS 中只有一个时钟，在下 CS 中有很多时钟。所有时钟都具有相同的机制，并且下部的时钟是同步的，也就是说，它们同时显示相同的时间。我们绘制了两个 CS 相对于彼此移动的三个连续位置。在第一幅图中，上部和下部时钟指针的位置按照惯例是相同的，因为我们是这样安排的。所有时钟都显示相同的时间。在第二幅图中，我们稍后会看到两个 CS 的相对位置。

But this is not the only possible answer. We can equally well imagine a moving clock having a different rhythm from one at rest. Let us now discuss this possibility without deciding, for the moment, whether or not clocks really change their rhythm in motion. What is meant by the statement that a moving clock changes its rhythm? Let us assume, for the sake of simplicity, that we have only one clock in the upper C.S. and many in the lower. A ll the clocks have the same mechanism, and the lower ones are synchronized, that is, they show the same time simultaneously. We have drawn three subsequent positions of the two C.S. moving relative to each other. In the first drawing the positions of the hands of the upper and lower clocks are, by convention, the same because we arranged them so. A ll the clocks show the same time. In the second drawing, we see the relative positions of the two C.S. some time later.

下部 CS 中的所有时钟都显示相同的时间，但上部 CS 中的时钟不合节奏。由于时钟相对于下部 CS 移动，节奏发生变化，时间也不同。在第三幅图中

A ll the clocks in the lower C.S. show the same time, but the clock in the upper C.S. is out of rhythm. The rhythm is changed and the time differs because the clock is moving relative to the lower C.S. In the third drawing

1 9 3

我们发现，随着时间的推移，指针位置的差异越来越大。

we see the difference in the positions of the hands increased with time.

处于下位坐标系的静止观察者会发现，移动的时钟会改变其节奏。当然，如果时钟相对于处于上位坐标系的静止观察者移动，也会发现同样的结果；在这种情况下，上位坐标系中必须有许多时钟，并且

A n observer at rest in the lower C.S. would find that a moving clock changes its rhythm. Certainly the same result could be found if the clock moved relative to an observer at rest in the upper C.S.; in this case there would have to be many clocks in the upper C.S. and

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下部只有一个。自然法则在两个相对运动的坐标系中必须是相同的。

only one in the lower. The laws of nature must be the same in both C.S. moving relative to each other.

在经典力学中，人们默认一个运动的时钟不会改变它的节奏。这似乎是显而易见的，几乎不值得一提。但没有什么是太明显的；如果我们真的想小心谨慎，我们应该分析物理学中迄今为止被视为理所当然的假设。

In classical mechanics it was tacitly assumed that a moving clock does not change its rhythm. This seemed so obvious that it was hardly worth mentioning. But nothing should be too obvious; if we wish to be really careful, we should analyse the assumptions, so far taken for granted, in physics.

不应仅仅因为一个假设与经典物理学的假设不同就认为它不合理。我们可以想象一个运动的时钟会改变它的节奏，只要这种变化的规律对所有惯性坐标系都相同

A n assumption should not be regarded as unreasonable simply because it differs from that of classical physics. We can well imagine that a moving clock changes its rhythm, so long as the law o f this change is the same for all inertial C.S.

再举一个例子。以码尺为例；这意味着，只要棍子静止在坐标系中，它的长度就是一码。现在它均匀移动，沿着代表坐标系的杆滑动。它的长度看起来还是一码吗？我们必须事先知道如何确定它的长度。只要棍子静止，它的两端就与坐标系上相距一码的标记相重合

Y et another example. Take a yardstick; this means that a stick is a yard in length as long as it is at rest in a C.S. Now it moves uniformly, sliding along the rod representing the C.S. W ill its length still appear to be one yard? We must know beforehand how to determine its length. As long as the stick was at rest, its ends coincided with markings one yard apart on the C.S.

由此我们得出结论：静止的木棍的长度为一码。我们怎样测量运动中的木棍呢？可以按如下方法进行。在给定时刻，两个观察者同时拍摄快照，一个拍摄木棍的起点，另一个拍摄木棍的末端。由于照片是同时拍摄的，我们可以比较 CS 杆上与运动木棍的起点和末端重合的标记。这样我们就可以确定它的长度。必须有两个观察者记录运动过程中不同部分同时发生的事件

From this we concluded: the length of the resting stick is one yard. How are we to measure this stick during motion? It could be done as follows. A t a given moment two observers simultaneously take snapshots, one o f the origin o f the stick and the other o f the end. Since the pictures are taken simultaneously, we can compare the marks on the C.S. rod with which the origin and the end o f the moving stick coincide. In this way we determine its length. There must be two observers to take note of simultaneous events in different parts of the

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给定 CS 没有理由相信这种测量结果会与静止的棍子的情况相同。由于必须同时拍摄照片，而我们已经知道，这是一个依赖于 CS 的相对概念，因此，在相对运动的不同 CS 中，这种测量结果很可能不同。

given C.S. There is no reason to believe that the result o f such measurements will be the same as in the case of a stick at rest. Since the photographs had to be taken simultaneously, which is, as we already know, a relative concept depending on the C.S., it seems quite possible that the results of this measurement will be different in different C.S. moving relative to each other.

我们可以想象，不仅运动的时钟会改变它的节奏，而且运动的棍子也会改变它的长度，只要变化的规律对所有的惯性坐标系都是相同的

We can well imagine that not only does the moving clock change its rhythm, but also that a moving stick changes its length, so long as the laws of the changes are the same for all inertial C.S.

我们只是在讨论一些新的可能性，而没有给出任何理由来假设它们。

We have only been discussing some new possibilities without giving any justification for assuming them.

我们记住：光速在所有惯性坐标系中都是相同的。这一事实与经典变换是无法调和的。圆一定在某处被打破。难道不能在这里做到这一点吗？我们能否假设运动时钟的节奏和运动杆的长度会发生这样的变化，以至于光速的恒定性将直接由这些假设得出？当然可以！这是相对论和经典物理学根本不同之处的第一个例子。我们的论证可以反过来：如果光速在所有坐标系中都是相同的，那么运动的杆必须改变其长度，运动的时钟必须改变其节奏，而支配这些变化的定律是严格确定的。

We remember: the velocity of light is the same in all inertial C.S. It is impossible to reconcile this fact with the classical transformation. The circle must be broken somewhere. C an it not be done just here? C an we not assume such changes in the rhythm o f the moving clock and in the length o f the moving rod that the constancy of the velocity o f light will follow directly from these assumptions? Indeed we can ! Here is the first instance in which the relativity theory and classical physics differ radically. O ur argument can be reversed: if the velocity of light is the same in all C.S., then moving rods must change their length, moving clocks must change their rhythm, and the laws governing these changes are rigorously determined.

这一切并没有什么神秘或不合理之处。在古典物理学中，人们总是假设运动中的时钟和静止的时钟具有相同的节奏，即 7-2

There is nothing mysterious or unreasonable in all this. In classical physics it was always assumed that clocks in motion and at rest have the same rhythm, that 7-2

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运动中的杆和静止中的杆的长度相同。如果光速在所有坐标系中都相同，如果相对论成立，那么我们必须牺牲这一假设。

rods in motion and at rest have the same length. I f the velocity of light is the same in all C.S., if the relativity theory is valid, then we must sacrifice this assumption.

根深蒂固的偏见很难摆脱，但别无他法。从相对论的角度来看，旧概念似乎有些武断。为什么像我们之前几页所说的那样，相信绝对时间对所有观察者在所有坐标系中都以相同的方式流动？

It is difficult to get rid o f deep-rooted prejudices, but there is no other way. From the point of view of the relativity theory the old concepts seem arbitrary. W hy believe, as we did some pages ago, in absolute time flowing in the same way for all observers in all C.S.?

为什么要相信距离不变？时间由时钟决定，空间坐标由杆决定，而它们决定的结果可能取决于这些时钟和杆在运动时的行为。没有理由相信它们会按照我们希望的方式运行。观察通过电磁场现象间接表明，运动的时钟会改变其节奏，杆会改变其长度，而根据机械现象，我们认为这种情况不会发生。我们必须接受每个 CS 中的相对时间概念，因为这是解决我们困难的最佳方法。从相对论发展而来的进一步科学进步表明，不应将这一新方面视为必然结果，因为该理论的优点太明显了。

Why believe in unchangeable distance? Tim e is determined by clocks, space co-ordinates by rods, and the result of their determination may depend on the behaviour o f these clocks and rods when in motion. There is no reason to believe that they will behave in the way we should like them to. Observation shows, indirectly, through the phenomena o f electromagnetic field, that a moving clock changes its rhythm, a rod its length, whereas on the basis of mechanical phenomena we did not think this happened. We must accept the concept of relative time in every C.S., because it is the best way out of our difficulties. Further scientific advance, developing from the theory o f relativity, shows that this new aspect should not be regarded as a malum necessarium, for the merits o f the theory are much too marked.

到目前为止，我们试图说明是什么导致了相对论的基本假设，以及该理论如何迫使我们通过以新的方式处理时间和空间来修改和改变经典变换。我们的目标是指出构成新物理和哲学观点基础的思想。这些思想很简单；但它们的形式

So far we have tried to show what led to the fundamental assumptions o f the relativity theory, and how the theory forced us to revise and to change the classical transformation by treating time and space in a new way. O u r aim is to indicate the ideas forming the basis of a new physical and philosophical view. These ideas are simple; but in the form in which they have been

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虽然在这里已经阐述了这些结论，但它们不足以得出定性的结论，也不足以得出定量的结论。

formulated here, they are insufficient for arriving at not only qualitative, but also quantitative conclusions.

我们必须再次使用我们的老方法，只解释主要思想，而陈述其他一些思想而无需证明。

We must again use our old method of explaining only the principal ideas and stating some of the others without proof.

为了讲清楚老物理学家（我们称之为0 ，相信经典变换）的观点和现代物理学家（我们称之为M ，了解相对论）的观点之间的区别，我们想象他们之间的对话。

To make clear the difference between the view of the old physicist, whom we shall call 0 and who believes in the classical transformation, and that of the modern physicist, whom we shall call M and who knows the relativity theory, we shall imagine a dialogue between them.

0我相信力学中的伽利略相对性原理，因为我知道，在两个相对匀速运动的坐标系中，力学定律是相同的，或者说，这些定律相对于经典变换是不变的。

0 . I believe in the Galilean relativity principle in mechanics, because I know that the laws of mechanics are the same in two C.S. moving uniformly relative to each other, or in other words, that these laws are invariant with respect to the classical transformation.

M。但相对性原理必须适用于我们外部世界的所有事件。不仅是力学定律，而且所有自然定律在相对匀速运动的坐标系中都必须相同。

M . But the relativity principle must apply to all events in our external world. Not only the laws of mechanics but all laws of nature must be the same in C.S. moving uniformly, relative to each other.

0。但是，在相对运动的坐标系中，自然界的所有定律怎么可能都相同呢？场方程，即麦克斯韦方程，对于经典变换来说并不是不变的。光速的例子清楚地表明了这一点。

0 . But how can all laws of nature possibly be the same in C.S. moving relative to each other? The field equations, that is, M axwell’s equations, are not invariant with respect to the classical transformation. This is clearly shown by the example o f the velocity of light.

按照经典变换，在两个相对运动的坐标系中，这个速度不应该相同。

According to the classical transformation, this velocity should not be the same in two C.S. moving relative to each other.

M。这仅仅表明经典变换不能应用，因为

M . This merely shows that the classical transformation cannot be applied, that the connection between

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两个坐标系必须不同；这样我们才不能像在这些变换定律中那样把坐标和速度联系起来。我们必须用新的定律来代替它们，并从相对论的基本假设中推导出来。我们不必为这个新的变换定律的数学表达式而烦恼，只要知道它与经典定律不同就行了。

two C.S. must be different; that we may not connect co-ordinates and velocities as is done in these transformation laws. We have to substitute new laws and deduce them from the fundamental assumptions of the theory of relativity. Let us not bother about the mathematical expression for this new transformation law, and be satisfied that it is different from the classical.

我们简称它为 洛伦兹变换。可以证明，麦克斯韦方程组，即场定律，对于洛伦兹变换是不变的，就像力学定律对于经典变换是不变的一样。

We shall call it briefly the Lorentz transformation. It can be shown that Maxwell’s equations, that is, the laws of field, are invariant with respect to the Lorentz transformation, just as the laws o f mechanics are invariant with respect to the classical transformation.

回想一下古典物理学中的情况。我们有坐标变换定律、速度变换定律，但力学定律对于两个相对匀速运动的坐标系是相同的。我们有空间变换定律，但没有时间变换定律，因为时间在所有坐标系中都是相同的。然而，在相对论中，情况有所不同。我们有不同于经典的空间、时间和速度变换定律。但同样，自然定律在所有相对匀速运动的坐标系中必须是相同的。自然定律必须是不变的，不是像以前那样相对于经典变换不变，而是相对于一种新型变换不变，即所谓的洛伦兹变换不变。

Remember how it was in classical physics. We had transformation laws for co-ordinates, transformation laws for velocities, but the laws of mechanics were the same for two C.S. moving uniformly, relative to each other. We had transformation laws for space, but not for time, because time was the same in all C.S. Here, however, in the relativity theory, it is different. We have transformation laws different from the classical for space, time, and velocity. But again the laws of nature must be the same in all C.S. moving uniformly, relative to each other. The laws of nature must be invariant, not, as before, with respect to the classical transformation, but with respect to a new type of transformation, the so-called Lorentz transformation.

在所有惯性坐标系中，相同的定律都是有效的，并且从一个坐标系到另一个坐标系的转变由洛伦兹变换给出。

In all inertial C.S. the same laws are valid and the transition from one C.S. to another is given by the Lorentz transformation.

0 . 我相信你的话，但我对此很感兴趣

0 . I take your word for it, but it would interest me

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了解经典变换和洛伦兹变换之间的区别。

to know the difference between the classical and Lorentz transformations.

M。您的问题最好用以下方式回答。列举一些经典变换的特征，我将尝试解释它们是否在洛伦兹变换中得以保留，如果不是，它们是如何改变的。

M . Your question is best answered in the following way. Quote some o f the characteristic features of the classical transformation and I shall try to explain whether or not they are preserved in the Lorentz transformation, and if not, how they are changed.

0。如果在我的 CS 中某个时间的某个点发生了某件事，那么相对于我的 CS 匀速移动的另一个 CS 中的观察者会为该事件发生的位置分配一个不同的数字，但时间当然是相同的。我们在所有 CS 中使用相同的时钟

0 . I f something happens at some point at some time in my C.S., then the observer in another C.S. moving uniformly, relative to mine, assigns a different number to the position in which this event occurs, but of course the same time. We use the same clock in all our C.S.

时钟是否走动并不重要。这对你来说也是这样吗？

and it is immaterial whether or not the clock moves. Is this also true for you?

M 。 不，不是。每个 CS 都必须配备自己的静止时钟，因为运动会改变节奏。

M . N o, it is not. Every C.S. must be equipped with its own clocks at rest, since motion changes the rhythm.

两个不同 CS 中的两个观察者不仅会为位置分配不同的编号，还会为该事件发生的时间分配不同的编号。

Two observers in two different C.S. will assign not only different numbers to the position, but also different numbers to the time at which this event happens.

0。这意味着时间不再是不变量。在经典变换中，所有 CS 中的时间始终相同。在洛伦兹变换中，它会发生变化，并且以某种方式表现得像旧变换中的坐标。我想知道距离如何？

0 . This means that the time is no longer an invariant. In the classical transformation it is always the same time in all C.S. In the Lorentz transformation it changes and somehow behaves like the co-ordinate in the old transformation. I wonder how it is with distance?

根据经典力学，刚性杆在运动或静止时都会保持其长度。现在这也是正确的吗？

According to classical mechanics a rigid rod preserves its length in motion or at rest. Is this also true now?

M 。 事实并非如此。事实上，根据洛伦兹变换，运动的棍子会沿着运动方向收缩，并且如果速度增加，收缩也会增加。棍子移动得越快，收缩越短

M . It is not. In fact, it follows from the Lorentz transformation that a moving stick contracts in the direction of the motion and the contraction increases if the speed increases. The faster a stick moves, the shorter

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看起来是这样。但这只发生在运动方向上。在我的画中，你可以看到一根移动的杆，当它以接近光速 90% 的速度移动时，它的长度会缩短一半。

it appears. But this occurs only in the direction of the motion. You see in my drawing a moving rod which shrinks to half its length, when it moves with a velocity approaching ca. 90 per cent of the velocity of light.

然而，正如我在图中试图说明的那样，在垂直于运动的方向上没有收缩。

There is no contraction, however, in the direction perpendicular to the motion, as I have tried to illustrate in my drawing.

0。这意味着移动时钟的节奏和移动棍子的长度取决于速度。

0 . This means that the rhythm of a moving clock and the length o f a moving stick depend on the speed.

但如何呢？

But how?

M 。 速度增加时，变化变得更加明显。根据洛伦兹变换，如果速度增加，一根棍子就会缩小到零

M . The changes become more distinct as the speed increases. It follows from the Lorentz transformation that a stick would shrink to nothing if its speed were to

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达到光速。同样，与沿着杆子移动的时钟相比，移动时钟的节奏会变慢，如果时钟以光速移动，也就是说，如果时钟是“好的”时钟，它就会停止。

reach that o f light. Similarly the rhythm of a moving clock is slowed down, compared to the clocks it passes along the rod, and would come to a stop if the clock were to move with the speed of light, that is, if the clock is a “ good” one.

0 。 这似乎与我们所有的经验相矛盾。我们知道汽车在行驶时不会变短，我们还知道司机总是可以把他的“好”手表与路上经过的手表进行比较，发现它们非常吻合，这与你的说法相反。

0 . This seems to contradict all our experience. We know that a car does not become shorter when in motion and we also know that the driver can always compare his “ good” watch with those he passes on the way, finding that they agree fairly well, contrary to your statement.

M。这当然是真的。但这些机械速度与光速相比都非常小，因此将相对论应用于这些现象是荒谬的。每个汽车司机都可以安全地应用经典物理学，即使他将车速提高十万倍。我们只能在速度接近光速时预期实验与经典变换之间会出现不一致。只有在非常快的速度下才能检验洛伦兹变换的有效性。

M . This is certainly true. But these mechanical velocities are all very small compared to that o f light, and it is, therefore, ridiculous to apply relativity to these phenomena. Every car driver can safely apply classical physics even if he increases his speed a hundred thousand times. We could only expect disagreement between experiment and the classical transformation with velocities approaching that of light. O nly with very great velocities can the validity of the Lorentz transformation be tested.

0 。 但还有另一个困难。根据力学原理，我可以想象物体的速度甚至比光速还要快。一个物体相对于一艘漂浮的船以光速运动，那么它相对于海岸的运动速度就大于光速。

0 . But there is yet another difficulty. According to mechanics I can imagine bodies with velocities even greater than that of light. A body moving with the velocity of light relative to a floating ship moves with a velocity greater than that of light relative to the shore.

当棍子的速度为光速时，如果棍子收缩为零，会发生什么情况？如果速度大于光速，我们很难期望它的长度为负数。

W hat will happen to the stick which shrank to nothing when its velocity was that o f light? We can hardly expect a negative length if the velocity is greater than that of light.

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M。真是没有道理这么讽刺！从相对论的角度来看，物体的速度不可能大于光速。

M . There is really no reason for such sarcasm! From the point of view of the relativity theory a material body cannot have a velocity greater than that o f light.

光速是一切物体速度的上限，如果物体相对于船的速度等于光速，那么物体相对于岸的速度也等于光速。

The velocity of light forms the upper limit of velocities for all material bodies. I f the speed of a body is equal to that o f light relative to a ship, then it will also be equal to that o f light relative to the shore.

简单的速度加减力学定律不再有效，或者更准确地说，它只对小速度近似有效，而对接近光速的速度则无效。表示光速的数字明确出现在洛伦兹变换中，并起着极限情况的作用，就像经典力学中的无限速度一样。这个更一般的理论并不与经典变换和经典力学相矛盾。相反，当速度较小时，我们重新获得了旧概念作为极限情况。从新理论的角度来看，古典物理学在哪些情况下有效以及其局限性在哪里是一目了然的。将相对论应用于汽车、轮船和火车的运动，就像在乘法表就足够的情况下使用计算机一样荒谬。

The simple mechanical law of adding and subtracting velocities is no longer valid or, more precisely, is only approximately valid for small velocities, but not for those near the velocity of light. The number expressing the velocity o f light appears explicitly in the Lorentz transformation, and plays the role o f a limiting case, like the infinite velocity in classical mechanics. This more general theory does not contradict the classical transformation and classical mechanics. O n the contrary, we regain the old concepts as a limiting case when the velocities are small. From the point o f view of the new theory it is clear in which cases classical physics is valid and wherein its limitations lie. It would be just as ridiculous to apply the theory of relativity to the motion o f cars, ships, and trains as to use a calculating machine where a multiplication table would be sufficient.

相对论与力学

R E L A T I V I T Y A N D M E C H A N IC S

相对论的产生源于必然性，源于旧理论中似乎无法摆脱的严重而深刻的矛盾。新理论的力量在于它的一致性和简单性。

The relativity theory arose from necessity, from serious and deep contradictions in the old theory from which there seemed no escape. The strength of the new theory lies in the consistency and simplicity with which it

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仅使用几个非常有说服力的假设就解决了所有这些困难。

solves all these difficulties, using only a few very convincing assumptions.

尽管该理论源于场问题，但它必须涵盖所有物理定律。这里似乎出现了一个困难。一方面是场定律，另一方面是力学定律，它们是完全不同的类型。电磁场方程相对于洛伦兹变换不变，而力学方程相对于经典变换不变。但相对论声称，所有自然定律都必须相对于洛伦兹变换不变，而不是相对于经典变换不变。后者只是当两个坐标系的相对速度非常小时，洛伦兹变换的一个特殊极限情况。如果是这样，经典力学必须改变以符合相对于洛伦兹变换不变的要求。

Although the theory arose from the field problem, it has to embrace all physical laws. A difficulty seems to appear here. The field laws on the one hand and the mechanical laws on the other are of quite different kinds. The equations of electromagnetic field are invariant with respect to the Lorentz transformation and the mechanical equations are invariant with respect to the classical transformation. But the relativity theory claims that all laws of nature must be invariant with respect to the Lorentz and not to the classical transformation. The latter is only a special, limiting case of the Lorentz transformation when the relative velocities o f two C.S. are very small. I f this is so, classical mechanics must change in order to conform with the demand of invariance with respect to the Lorentz transformation.

或者说，如果速度接近光速，经典力学就不再成立。从一个坐标系到另一个坐标系只能存在一种变换，即洛伦兹变换。

O r, in other words, classical mechanics cannot be valid if the velocities approach that o f light. O nly one transformation from one C.S. to another can exist, namely, the Lorentz transformation.

改变经典力学很简单，只要它既不与相对论相矛盾，也不与通过观察获得并由经典力学解释的大量材料相矛盾。旧力学适用于小速度，并构成新力学的极限情况。

It was simple to change classical mechanics in such a way that it contradicted neither the relativity theory nor the wealth o f material obtained by observation and explained by classical mechanics. The old mechanics is valid for small velocities and forms the limiting case of the new one.

考虑一下相对论对经典力学的改变，这将会很有趣。这也许会引导我们得出一些

It would be interesting to consider some instance o f a change in classical mechanics introduced by the relativity theory. This might, perhaps, lead us to some

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可以通过实验来证明或反驳的结论。

conclusions which could be proved or disproved by experiment.

假设一个物体具有一定的质量，沿直线运动，并受到沿运动方向的外力作用。我们知道，外力与速度的变化成正比。或者更明确地说，一个物体在一秒钟内的速度从每秒 100 英尺增加到 101 英尺，或从每秒 100 英里增加到 100 英里 1 英尺，或从每秒 180,000 英里增加到 180,000 英里，这些都无关紧要。

Let us assume a body, having a definite mass, moving along a straight line, and acted upon by an external force in the direction of the motion. The force, as we know, is proportional to the change o f velocity. O r, to be more explicit, it does not matter whether a given body increases its velocity in one second from 100 to 101 feet per second, or from 100 miles to 100 miles and one foot per second or from 180,000 miles to 180,000

每秒一英里和一英尺。作用于特定物体的力对于相同时间内的相同速度变化总是相同的。

miles and one foot per second. The force acting upon a particular body is always the same for the same change of velocity in the same time.

从相对论的角度来看，这句话是正确的吗？绝对不是！这条定律只对小速度有效。根据相对论，对于接近光速的大速度，定律是什么呢？如果速度很大，就需要非常强的力来增加它。将大约每秒 100 英尺的速度和接近光速的速度增加一英尺每秒完全是两码事。速度越接近光速，增加就越困难。当速度等于光速时，就不可能再增加。因此，相对论带来的变化并不令人惊讶。光速是所有速度的上限。无论多大，任何有限的力都不能使速度超过这个极限。代替旧的将力和速度变化联系起来的机械定律，一个更强大的理论

Is this sentence true from the point of view of the relativity theory? By no means ! This law is valid only for small velocities. W hat, according to the relativity theory, is the law for great velocities, approaching that o f light? I f the velocity is great, extremely strong forces are required to increase it. It is not at all the same thing to increase by one foot per second a velocity o f about 100 feet per second or a velocity approaching that o f light. The nearer a velocity is to that o f light the more difficult it is to increase. When a velocity is equal to that of light it is impossible to increase it further. Thus, the changes brought about by the relativity theory are not surprising. The velocity o f light is the upper limit for all velocities. No finite force, no matter how great, can cause an increase in speed beyond this limit. In place of the old mechanical law connecting force and change of velocity, a more

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复杂的出现了。从我们的新观点来看，经典力学很简单，因为在几乎所有的观察中，我们处理的速度都比光速小得多。

complicated one appears. From our new point of view classical mechanics is simple because in nearly all observations we deal with velocities much smaller than that of light.

静止的物体具有一定的质量，称为 静止质量。

A body at rest has a definite mass, called the rest mass.

我们从力学中知道，每个物体都会抵抗其运动的变化；质量越大，阻力越大，质量越小，阻力越小。但在相对论中，我们还有更多内容。物体不仅在静止质量较大时抵抗变化的阻力更大，而且在速度较大时也抵抗变化的阻力更大。速度接近光速的物体对外力的抵抗力非常强。在经典力学中，给定物体的阻力是不可改变的，仅由其质量表征。在相对论中，它取决于静止质量和速度。当速度接近光速时，阻力会变得无限大。

We know from mechanics that every body resists a change in its motion; the greater the mass, the stronger the resistance, and the weaker the mass, the weaker the resistance. But in the relativity theory, we have something more. Not only does a body resist a change more strongly if the rest mass is greater, but also if its velocity is greater. Bodies with velocities approaching that of light would offer a very strong resistance to external forces. In classical mechanics the resistance o f a given body was something unchangeable, characterized by its mass alone. In the relativity theory it depends on both rest mass and velocity. The resistance becomes infinitely great as the velocity approaches that of light.

刚刚引用的结果使我们能够用实验检验该理论。速度接近光速的抛射物是否如理论所预测的那样抵抗外力的作用？由于相对论的陈述在这方面具有定量特征，如果我们能够实现速度接近光速的抛射物，我们就可以证实或反驳该理论。

The results just quoted enable us to put the theory to the test of experiment. Do projectiles with a velocity approaching that of light resist the action of an external force as predicted by the theory? Since the statements of the relativity theory have, in this respect, a quantitative character, we could confirm or disprove the theory if we could realize projectiles having a speed approaching that of light.

事实上，我们在自然界中发现了具有这种速度的抛射物。放射性物质的原子，例如镭，充当电池，以极高的速度发射抛射物。我们不必详述，只能引用

Indeed, we find in nature projectiles with such velocities. Atoms of radioactive matter, radium for instance, act as batteries which fire projectiles with enormous velocities. Without going into detail we can quote only

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这是现代物理学和化学的一个非常重要的观点。宇宙中的所有物质都由几种基本粒子组成。这就像在一个城镇里看到不同大小、结构和建筑风格的建筑物，但从棚屋到摩天大楼，只使用了很少几种不同的砖块，所有建筑物都是一样的。因此，我们物质世界的所有已知元素——从最轻的氢到最重的铀——都是由同一种砖块构成的，也就是说，由同一种基本粒子构成。

one o f the very important views of modern physics and chemistry. A ll matter in the universe is made up o f elementary particles o f only a few kinds. It is like seeing in one town buildings of different sizes, construction and architecture, but from shack to skyscraper only very few different kinds of bricks were used, the same in all the buildings. So all known elements o f our material world— from hydrogen the lightest, to uranium the heaviest— are built of the same kinds of bricks, that is, the same kinds o f elementary particles.

最重的元素、最复杂的建筑都是不稳定的，它们会分解，或者说，具有放射性。有些砖块，即构成放射性原子的基本粒子，有时会以非常快的速度抛出，接近光速。根据我们目前的观点，经过大量实验证实，元素（例如镭）的原子是一种复杂的结构，放射性分解就是揭示更简单的砖块（基本粒子）的原子组成的现象之一。

The heaviest elements, the most complicated buildings, are unstable and they disintegrate or, as we say, are radioactive. Some o f the bricks, that is, the elementary particles of which the radioactive atoms are constructed, are sometimes thrown out with a very great velocity, approaching that o f light. A n atom of an element, say radium, according to our present views, confirmed by numerous experiments, is a complicated structure, and radioactive disintegration is one of those phenomena in which the composition of atoms from still simpler bricks, the elementary particles, is revealed.

通过非常巧妙和复杂的实验，我们可以发现粒子如何抵抗外力的作用。实验表明，这些粒子提供的阻力取决于速度，就像相对论所预见的那样。在许多其他情况下，当可以检测到阻力对速度的依赖性时，理论和实验之间完全一致。我们看到一次

By very ingenious and intricate experiments we can find out how the particles resist the action of an external force. The experiments show that the resistance offered by these particles depends on the velocity, in the way foreseen by the theory of relativity. In many other cases, where the dependence o f the resistance upon the velocity could be detected, there was complete agreement between theory and experiment. We see once

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更多的是科学创造性劳动的本质特征：通过理论预测某些事实，并通过实验来证实。

more the essential features of creative work in science: prediction of certain facts by theory and their confirmation by experiment.

这一结果进一步表明了重要的概括。静止的物体有质量，但没有动能，即运动能量。运动的物体既有质量又有动能。它比静止的物体更能抵抗速度的变化。似乎运动物体的动能增加了它的抵抗力。如果两个物体的静止质量相同，动能较大的物体对外力作用的抵抗力更大。

This result suggests a further important generalization. A body at rest has mass but no kinetic energy, that is, energy of motion. A moving body has both mass and kinetic energy. It resists change o f velocity more strongly than the resting body. It seems as though the kinetic energy o f the moving body increases its resistance. I f two bodies have the same rest mass, the one with the greater kinetic energy resists the action of an external force more strongly.

想象一个装有球的盒子，盒子和球都静止在我们的坐标系中。为了移动它，增加它的速度，需要一定的力。但是，当球像气体分子一样在盒子内快速地向各个方向移动，平均速度接近光速时，同样的力能在相同的时间内使速度增加相同的量吗？由于球的动能增加，现在需要更大的力，从而增强盒子的阻力。能量，无论如何，动能，以与有重量的物体相同的方式抵抗运动。所有类型的能量都是如此吗？

Imagine a box containing balls, with the box as well as the balls at rest in our C.S. T o move it, to increase its velocity, some force is required. But will the same force increase the velocity by the same amount in the same time with the balls moving about quickly and in all directions inside the box, like the molecules o f a gas, with an average speed approaching that of light? A greater force will now be necessary because of the increased kinetic energy o f the balls, strengthening the resistance of the box. Energy, at any rate kinetic energy, resists motion in the same way as ponderable masses. Is this also true of all kinds o f energy?

相对论从其基本假设出发，对这个问题推导出一个明确而令人信服的答案，而且这个答案同样具有定量性：所有能量都抵抗运动的变化；所有能量的行为都像物质；一块铁在炽热时比冷却时重；辐射穿过

The theory o f relativity deduces, from its fundamental assumption, a clear and convincing answer to this question, an answer again of a quantitative character: all energy resists change o f motion; all energy behaves like matter; a piece o f iron weighs more when red-hot than when cool; radiation travelling through

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太空中从太阳发射的辐射包含能量，因此具有质量；太阳和所有辐射恒星通过发射辐射而失去质量。这一结论具有相当的普遍性，是相对论的一项重要成就，符合所有已对其进行检验的事实。

space and emitted from the sun contains energy and therefore has mass; the sun and all radiating stars lose mass by emitting radiation. This conclusion, quite general in character, is an important achievement of the theory of relativity and fits all facts upon which it has been tested.

古典物理学引入了两种物质：物质和能量。前者有重量，而后者没有重量。在古典物理学中，我们有两条守恒定律：一条是物质守恒定律，另一条是能量守恒定律。我们已经问过，现代物理学是否仍然坚持这种两种物质和两条守恒定律的观点。答案是：“不”。根据相对论，质量和能量之间没有本质区别。能量有质量，质量代表能量。我们没有两条守恒定律，只有一条，即质能守恒定律。这种新观点在物理学的进一步发展中被证明是非常成功的，并且卓有成效。

Classical physics introduced two substances: matter and energy. The first had weight, but the second was weightless. In classical physics we had two conservation laws: one for matter, the other for energy. We have already asked whether modern physics still holds this view of two substances and the two conservation laws. The answer is: “ N o ” . According to the theory of relativity, there is no essential distinction between mass and energy. Energy has mass and mass represents energy. Instead of two conservation laws we have only one, that of mass-energy. This new view proved very successful and fruitful in the further development of physics.

为什么能量具有质量，质量代表能量这一事实这么长时间以来一直被掩盖？一块热铁的重量是否大于一块冷铁的重量？这个问题的答案现在是

How is it that this fact of energy having mass and mass representing energy remained for so long obscured? Is the weight o f a piece of hot iron greater than that of a cold piece? The answer to this question is now

“是”，但第 43 页却写着“否”。这两个答案之间的页数显然不足以掩盖这一矛盾。

“ Y e s” , but on p. 43 it was “ N o ” . The pages between these two answers are certainly not sufficient to cover this contradiction.

我们在这里遇到的困难与我们以前遇到的困难是一样的。相对论所预测的质量变化是不可测量的，甚至无法通过直接称量最重的物体来检测。

The difficulty confronting us here is of the same kind as we have met before. The variation o f mass predicted by the theory of relativity is immeasurably small and cannot be detected by direct weighing on even the most

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灵敏的尺度。能量不是无重量的，这一证据可以通过许多非常确凿但间接的方式获得。

sensitive scales. The proof that energy is not weightless can be gained in many very conclusive, but indirect, ways.

缺乏直接证据的原因是物质和能量之间的交换率非常小。

The reason for this lack of immediate evidence is the very small rate of exchange between matter and energy.

与质量相比，能量就像贬值的货币与高价值货币相比。举个例子就清楚了。能够将三万吨水转化为蒸汽的热量大约重一克！长期以来，能量被认为是无重量的，只是因为它所代表的质量非常小。

Compared to mass, energy is like a depreciated currency compared to one of high value. A n example will make this clear. The quantity of heat able to convert thirty thousand tons of water into steam would weigh about one g ra m ! Energy was regarded as weightless for so long simply because the mass which it represents is so small.

旧的能量物质是相对论的第二个牺牲品，第一个牺牲品是光波传播的介质。

The old energy-substance is the second victim of the theory of relativity. The first was the medium through which light waves were propagated.

相对论的影响远远超出了它所引发的问题。它消除了场论的困难和矛盾；它制定了更普遍的力学定律；它用一个守恒定律取代了两个守恒定律；它改变了我们传统的绝对时间概念。它的有效性并不局限于物理学的一个领域；它形成了一个涵盖所有自然现象的一般框架。

The influence of the theory of relativity goes far beyond the problem from which it arose. It removes the difficulties and contradictions of the field theory; it formulates more general mechanical laws; it replaces two conservation laws by one; it changes our classical concept of absolute time. Its validity is not restricted to one domain of physics; it forms a general framework embracing all phenomena of nature.

空间控制技术

T H E T IM E -S P A C E C O N T IN U U M

“法国大革命于 1789 年 7 月 14 日在巴黎爆发。”这句话陈述了事件发生的地点和时间。第一次听到这句话的人可能会明白“巴黎”是什么意思：它是地球上一座位于长岛上的城市。2°

“ The French revolution began in Paris on the 14th of Ju ly 1789.” In this sentence the place and time of an event are stated. Hearing this statement for the first time, one who does not know what “ Paris” means could be taught: it is a city on our earth situated in long. 2°

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东经 49°，北纬 49°。这两个数字表示事件发生的地点，“1789 年 7 月 14 日”表示事件发生的时间。在物理学中，比在历史学中，准确描述事件发生的时间和地点非常重要，因为这些数据构成了定量描述的基础。

East and lat. 49° North. The two numbers would then characterize the place, and “ 14th of Ju ly 1789” the time, at which the event took place. In physics, much more than in history, the exact characterization o f when and where an event takes place is very important, because these data form the basis for a quantitative description.

为简单起见，我们先前只考虑沿直线的运动。我们的坐标系是一个有原点但没有终点的刚性杆。让我们保留这个限制。取杆上的不同点；它们的位置只能用一个数字来表征，即该点的坐标。说某个点的坐标是 7.586 英尺，意味着它距离杆的原点 7.586 英尺。相反，如果有人给我任意数字和单位，我总能在杆上找到一个与这个数字相对应的点。我们可以说：杆上的一个确定点对应于每个数字，而一个确定的数字对应于每个点。数学家在以下句子中表达了这一事实：杆上的所有点形成 一维连续体。在杆上的每个点附近都存在一个点。我们可以通过任意小的步长连接杆上两个遥远的点。因此，连接遥远点的步长的任意小是连续体的特征。

For the sake o f simplicity, we considered previously only motion along a straight line. A rigid rod with an origin but no end-point was our C.S. Let us keep this restriction. Take different points on the rod; their positions can be characterized by one number only, by the co-ordinate of the point. T o say the co-ordinate of a point is 7.586 feet means that its distance is 7.586 feet from the origin of the rod. If, on the contrary, someone gives me any number and a unit, I can always find a point on the rod corresponding to this number. We can state: a definite point on the rod corresponds to every number, and a definite number corresponds to every point. This fact is expressed by mathematicians in the following sentence: all points on the rod form a one-dimensional continuum. There exists a point arbitrarily near every point on the rod. We can connect two distant points on the rod by steps as small as we wish. Thus the arbitrary smallness of the steps connecting distant points is characteristic of the continuum.

现在再举一个例子。我们有一个平面，或者，如果你喜欢更具体一点的话，是一个长方形桌子的表面。这个桌子上一个点的位置

Now another example. We have a plane, or, if you prefer something more concrete, the surface of a rectangular table. The position of a point on this table

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可以用两个数字来表征，而不是像以前一样用一个数字来表征。这两个数字是到桌子两个垂直边的距离。不是一个数字，而是一对数字对应于平面上的每个点；一个确定的点对应于每一对数字。换句话说：平面是一个二维 连续体。在平面上的每个点附近都存在任意点。两个远距离点可以通过一条曲线连接，该曲线分成任意小的台阶。因此，连接两个远距离点的台阶的任意小（每个台阶都可以用两个数字表示）也是二维连续体的特征。

can be characterized by two numbers and not, as before, by one. The two numbers are the distances from two perpendicular edges of the table. Not one number, but a pair of numbers corresponds to every point on the plane; a definite point corresponds to every pair of numbers. In other words: the plane is a two-dimensional continuum. There exist points arbitrarily near every point on the plane. Two distant points can be connected by a curve divided into steps as small as we wish. Thus the arbitrary smallness of the steps connecting two distant points, each of which can be represented by two numbers, is again characteristic of a two-dimensional continuum.

再举一个例子。假设您希望将房间视为您的 CS 这意味着您想要描述相对于房间刚性墙壁的所有位置。如果灯处于静止状态，灯端点的位置可以用三个数字来描述：其中两个数字确定与两个垂直墙壁的距离，第三个数字确定与地板或天花板的距离。三个确定的数字对应于空间中的每个点；空间中的确定点

One more example. Imagine that you wish to regard your room as your C.S. This means that you want to describe all positions with respect to the rigid walls o f the room. The position of the end-point of the lam p, if the lamp is at rest, can be described by three numbers: two o f them determine the distance from two perpendicular walls, and the third that from the floor or ceiling. Three definite numbers correspond to every point of the space; a definite point in space

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每三个数字对应一个。这句话可以表达为：我们的空间是一个 三维连续体。空间中每个点附近都存在一些点。同样，连接远点的步长任意小，每个点都用三个数字表示，这是三维连续体的特征。

corresponds to every three numbers. This is expressed by the sentence: O u r space is a three-dimensional continuum. There exist points very near every point of the space. Again the arbitrary smallness o f the steps connecting the distant points, each of them represented by three numbers, is characteristic o f a three-dimensional continuum.

但这些都不是物理学。回到物理学，必须考虑物质粒子的运动。

But all this is scarcely physics. To return to physics, the motion o f material particles must be considered.

为了观察和预测自然事件，我们不仅要考虑物理事件的地点，还要考虑事件发生的时间。让我们再举一个非常简单的例子。

T o observe and predict events in nature we must consider not only the place but also the time of physical happenings. Let us again take a very simple example.

一块小石头，可以看作是一个粒子，从一座塔上掉下来。想象这座塔有 256 英尺高。自伽利略时代以来，我们就能预测石头掉下后任意时刻的坐标。这里有一个“时间表”

A small stone, which can be regarded as a particle, is dropped from a tower. Imagine the tower 256 feet high. Since Galileo’s time we have been able to predict the co-ordinate of the stone at any arbitrary instant after it was dropped. Here is a “ timetable”

描述石头在0、1、2、3和4秒后的位置。

describing the positions o f the stone after 0, 1, 2, 3, and 4 seconds.

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时间

Time in

海拔高度

Elevation from

秒

seconds

地面以英尺为单位

the ground in feet

256

240

192

112

我们的“时间表”里登记了五个事件，每个事件用两个数字表示，时间和空间

Five events are registered in our “ timetable” , each represented by two numbers, the time and space co

-每个事件的坐标。第一个事件是石头在零秒时从地面以上 256 英尺处落下。第二个事件是石头与地面以上 240 英尺处的刚性杆（塔）重合。这发生在第一秒之后。最后一个事件是石头与地球重合。

-ordinates o f each event. The first event is the dropping of the stone from 256 feet above the ground at the zero second. The second event is the coincidence of the stone with our rigid rod (the tower) at 240 feet above the ground. This happens after the first second. The last event is the coincidence of the stone with the earth.

我们可以代表从我们

We could represent the knowledge gained from our

以不同的方式表示“时间表”。我们可以将“时间表”中的五对数字表示为表面上的五个点。让我们首先建立一个刻度。一个段对应一英尺，另一个段对应一秒。例如：

“ timetable” in a different way. We could represent the five pairs o f numbers in the “ timetable” as five points on a surface. Let us first establish a scale. One segment will correspond to a foot and another to a second. For example:

然后我们画两条垂直线，水平线称为时间轴，垂直线称为空间轴。我们立即看到我们的“时间表”可以用时空平面上的五个点来表示。

We then draw two perpendicular lines, calling the horizontal one, say, the time axis and the vertical one the space axis. We see immediately that our “ timetable” can be represented by five points in our time-space plane.

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点与空间轴的距离代表我们“时间表”第一列中记录的时间坐标，与时间轴的距离代表它们的空间坐标。

The distances of the points from the space axis represent the time co-ordinates as registered in the first column of our “ timetable” , and the distances from the time axis their space co-ordinates.

完全相同的东西可以用两种不同的方式表达：通过“时间表”和通过平面上的点。每一种都可以从另一种构建。在这两种表示方式之间进行选择只是个人喜好问题，因为它们实际上是等价的。

Exactly the same thing is expressed in two different ways: by the “ timetable” and by the points on the plane. Each can be constructed from the other. The choice between these two representations is merely a matter of taste, for they are, in fact, equivalent.

现在让我们更进一步。想象一个更好的

Let us now go one step farther. Imagine a better

“时间表”给出的不是每一秒的位置，而是每百分之一或千分之一秒的位置。

“ timetable” giving the positions not for every second, but for, say, every hundredth or thousandth o f a second.

这样，我们的时空平面上就会有很多点。最后，如果每个瞬间的位置都是给定的，或者如数学家所说，如果空间坐标

We shall then have very many points on our time-space plane. Finally, if the position is given for every instant or, as the mathematicians say, if the space co-ordinate

作为 t 2 的函数给出

is given as a function o f t 2

im e，那么我们的点集

im e, then our set o f points

变成一条连续的线。因此，我们的下一幅画不仅像之前一样代表一个片段，而且代表了对运动的完整了解。

becomes a continuous line. O u r next drawing therefore represents not just a fragment as before, but a complete knowledge o f the motion.

沿刚性杆（塔）的运动，即一维空间中的运动，在这里表示为二维时空连续体中的曲线。

T he motion along the rigid rod (the tower), the motion in a one-dimensional space, is here represented as a curve in a two-dimensional time-space continuum .

时空连续体中的每个点都对应一对数字，其中一个表示时间，另一个表示空间坐标。相反，时空平面上的一个确定点对应于描述事件的每一对数字。

T o every point in our time-space continuum there corresponds a pair o f numbers, one o f which denotes the tim e, and the other the space, co-ordinate. Conversely: a definite point in our time-space plane corresponds to every pair o f numbers characterizing an event.

两个相邻的点代表两个事件、两件发生的事情，发生在略有不同的地点和略有不同的时刻。

Tw o adjacent points represent two events, two happenings, at slightly different places and at slightly different instants.

你可以这样反驳我们的表述：

Y ou could argue against our representation thus:

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用一个片段来表示一个时间单位，将其与空间机械地结合起来，从两个一维连续体形成二维连续体，这是没有意义的。但是，你也会同样强烈地反对所有表示例如去年夏天纽约市气温变化的图表，或者反对那些表示过去几年生活成本变化的图表，因为在每种情况下都使用了完全相同的方法。在温度图中，一维温度连续体与一维时间连续体结合成二维温度-时间连续体。

there is little sense in representing a unit of time by a segment, in combining it mechanically with the space, forming the two-dimensional continuum from the two one-dimensional continua. But you would then have to protest just as strongly against all the graphs representing, for example, the change of temperature in New York City during last summer, or against those representing the changes in the cost of living during the last few years, since the very same method is used in each of these cases. In the temperature graphs the one-dimensional temperature continuum is combined with the one-dimensional time continuum into the two-dimensional temperature-time continuum.

让我们回到从 256 英尺高的塔上落下的粒子。我们的运动图形是一种有用的惯例，因为它描述了粒子在任意时刻的位置。知道粒子如何运动后，我们想再次描绘它的运动。

Let us return to the particle dropped from a 256-foot tower. O ur graphic picture of motion is a useful convention since it characterizes the position of the particle at an arbitrary instant. Knowing how the particle moves, we should like to picture its motion once more.

我们可以用两种不同的方式来做到这一点。

We can do this in two different ways.

我们记得粒子在一维空间中随时间改变位置的图像。

We remember the picture o f the particle changing its position with time in the one-dimensional space.

我们将运动描绘为一维空间连续体中的一系列事件。我们不将时间和空间混为一谈，而是采用位置随时间变化的动态图像。

We picture the motion as a sequence o f events in the one-dimensional space continuum. We do not mix time and space, using a dynamic picture in which positions change with time.

但我们可以用不同的方式来描绘相同的运动。我们可以形成一幅静态图像，考虑二维时空连续体中的曲线。现在，运动被表示为存在于二维时空连续体中的某种东西，

But we can picture the same motion in a different way. We can form a static picture, considering the curve in the two-dimensional time-space continuum. Now the motion is represented as something which is, which exists in the two-dimensional time-space continuum,

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而不是像一维空间连续体中发生变化的东西。

and not as something which changes in the one-dimensional space continuum.

这两幅图完全相同，选择其中一幅仅仅只是习惯和品味的问题。

Both these pictures are exactly equivalent, and preferring one to the other is merely a matter of convention and taste.

这里所说的关于运动的两种图像与相对论毫无关系。这两种表述都可以同等使用，尽管古典物理学更倾向于将运动描述为空间中发生的事情而不是存在于时空中的动态图像。但相对论改变了这种观点。它明显倾向于静态图像，并发现这种将运动描述为存在于时空中的东西的表述是更方便、更客观的现实图像。

Nothing that has been said here about the two pictures o f the motion has anything whatever to do with the relativity theory. Both representations can be used with equal right, though classical physics favoured rather the dynamic picture describing motion as happenings in space and not as existing in time-space. But the relativity theory changes this view. It was distinctly in favour of the static picture and found in this representation of motion as something existing in time-space a more convenient and more objective picture o f reality.

我们还要回答这个问题：为什么这两幅图从经典物理学的角度看是等价的，但从相对论的角度看却不等价？

We still have to answer the question: why are these two pictures, equivalent from the point o f view o f classical physics, not equivalent from the point of view o f the relativity theory?

如果再次考虑两个相对于彼此均匀运动的 CS，我们就能理解答案。

The answer will be understood if two C.S. moving uniformly, relative to each other, are again taken into account.

根据经典物理学，两个坐标系中的观察者

According to classical physics, observers in two C.S.

相对运动的粒子会为某一事件分配不同的空间坐标，但时间坐标相同。因此，在我们的例子中，粒子与地球的重合在我们选择的坐标系中用时间坐标“4”和空间坐标“0”来表示。根据经典力学，石头在经过 10 ...

moving uniformly, relative to each other, will assign different space co-ordinates, but the same time coordinate, to a certain event. Thus in our example, the coincidence of the particle with the earth is characterized in our chosen C.S. by the time co-ordinate “ 4 ” and by the space co-ordinate “ 0 ” . According to classical mechanics, the stone will still reach the earth after

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对于相对于所选 CS 匀速运动的观察者来说，需要四秒。但是，该观察者会将距离参考到他的 CS，并且通常会将不同的空间坐标与碰撞事件联系起来，尽管时间坐标对于他以及对于所有其他相对于彼此匀速运动的观察者来说都是相同的。

four seconds for an observer moving uniformly, relative to the chosen C.S. But this observer will refer the distance to his C.S. and will, in general, connect different space co-ordinates with the event of collision, although the time co-ordinate will be the same for him and for all other observers moving uniformly, relative to each other.

经典物理学只知道所有观察者都存在“绝对”时间流。对于每个坐标系，二维连续体可以分为两个一维连续体：时间和空间。由于“绝对”时间流的存在，

Classical physics knows only an “ absolute” time flow for all observers. For every C.S. the two-dimensional continuum can be split into two one-dimensional continua: time and space. Because of the “ absolute”

由于时间的特性，从“静态”运动图像到“动态”运动图像的转变在经典物理学中具有客观意义。

character of time, the transition from the “ static” to the “ dynam ic” picture o f motion has an objective meaning in classical physics.

但我们已经确信，经典变换在物理学中不应广泛使用。从实用的角度来看，它仍然适用于小速度，但不适合解决基本物理问题。

But we have already allowed ourselves to be convinced that the classical transformation must not be used in physics generally. From a practical point of view it is still good for small velocities, but not for settling fundamental physical questions.

根据相对论，对于所有观察者来说，石头与地球碰撞的时间不会相同。在两个坐标系中，时间坐标和空间坐标会有所不同，如果相对速度接近光速，时间坐标的变化会非常明显。二维连续体不能像在经典物理学中那样分裂成两个一维连续体。在确定另一个坐标系中的时空坐标时，我们不能分别考虑空间和时间。从

According to the relativity theory the time of the collision of the stone with the earth will not be the same for all observers. The time co-ordinate and the space co-ordinate will be different in two C.S., and the change in the time co-ordinate will be quite distinct if the relative velocity is close to that o f light. The two-dimensional continuum cannot be split into two one-dimensional continua as in classical physics. We must not consider space and time separately in determining the time-space co-ordinates in another C.S. The splitting o f the two-dimensional continuum into two one-dimensional ones seems, from the point o f view

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相对论是一种任意的程序，没有客观意义。

of the relativity theory, to be an arbitrary procedure without objective meaning.

对于不局限于直线的运动，我们刚才所说的一切都很容易概括。事实上，描述自然界事件必须使用四个数字，而不是两个数字。我们通过物体及其运动构想的物理空间有三个维度，位置由三个数字表示。事件的瞬间是第四个数字。

It will be simple to generalize all that we have just said for the case o f motion not restricted to a straight line. Indeed, not two, but four, numbers must be used to describe events in nature. O ur physical space as conceived through objects and their motion has three dimensions, and positions are characterized by three numbers. The instant of an event is the fourth number.

每个事件都对应着四个确定的数字；一个确定的事件对应着任何四个数字。因此：事件世界形成一个四维 连续体。这没有什么神秘的，最后一句话对于经典物理学和相对论同样适用。当考虑两个相对于彼此运动的 CS 时，就会发现一个优点和一个缺点。房间在移动，室内和室外的观察者确定相同事件的时空坐标。同样，古典物理学家将四维连续体分为三维空间和一维时间连续体。老物理学家只关心空间变换，因为时间对他来说是绝对的。他发现将四维世界连续体分裂成空间和时间是自然而方便的。但是从相对论的角度来看，时间和空间都会随着从一个坐标系转换到另一个坐标系而改变，而洛伦兹变换考虑了我们四维事件世界的四维时空连续体的变换特性。

Four definite numbers correspond to every event; a definite event corresponds to any four numbers. Therefore : The world of events forms a four-dimensional continuum. There is nothing mysterious about this, and the last sentence is equally true for classical physics and the relativity theory. A gain, a difference is revealed when two C.S. moving relatively to each other are considered. The room is moving, and the observers inside and outside determine the time-space co-ordinates of the same events. Again, the classical physicist splits the four-dimensional continua into the three-dimensional spaces and the one-dimensional time-continuum. The old physicist bothers only about space transformation, as time is absolute for him. H e finds the splitting of the four-dimensional world-continua into space and time natural and convenient. But from the point o f view of the relativity theory, time as well as space is changed by passing from one C.S. to another, and the Lorentz transformation considers the transformation properties of the four-dimensional time-space continuum of our four-dimensional world of events.

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事件世界可以用一幅随时间变化并投射到三维空间背景中的图像来动态描述。但它也可以用一幅投射到四维时空连续体背景的静态图像来描述。从经典物理学的角度来看，动态和静态这两幅图像是等价的。

The world o f events can be described dynamically by a picture changing in time and thrown on to the background o f the three-dimensional space. But it can also be described by a static picture thrown on to the background of a four-dimensional time-space continuum. From the point of view of classical physics the two pictures, the dynamic and the static, are equivalent.

但从相对论的观点来看，静态图像更方便、更客观。

But from the point of view of the relativity theory the static picture is the more convenient and the more objective.

即使在相对论中，如果我们愿意，我们仍然可以使用动态图像。但我们必须记住，这种时间和空间的划分没有客观意义，因为时间不再是“绝对的”。

Even in the relativity theory we can still use the dynamic picture if we prefer it. But we must remember that this division into time and space has no objective meaning since time is no longer “ absolute” .

我们仍将使用“动态”，而不是“静态”

We shall still use the “ dynam ic” and not the “ static”

在接下来的几页中，我们将使用更详细的语言来阐述这一点，同时要牢记其局限性。

language in the following pages, bearing in mind its limitations.

广义相对论

G E N E R A L R E L A T I V I T Y

仍有一点需要澄清。最基本的问题之一尚未解决：惯性系统是否存在？我们已经了解了一些自然定律、它们相对于洛伦兹变换的不变性以及它们对所有相对匀速运动的惯性系统的有效性。我们有定律，但不知道该参考哪个框架。

There still remains one point to be cleared up. O ne o f the most fundamental questions has not been settled as yet: does an inertial system exist? We have learned something about the laws of nature, their invariance with respect to the Lorentz transformation, and their validity for all inertial systems moving uniformly, relative to each other. We have the laws but do not know the frame to which to refer them.

为了更好地了解这个困难，让我们采访这位古典物理学家并问他一些简单的问题：

In order to be more aware o f this difficulty, let us interview the classical physicist and ask him some simple questions:

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“什么是惯性系统？”

“ What is an inertial system?”

“ 它是力学定律有效的 CS。

“ It is a C.S. in which the laws of mechanics are valid.

不受外力作用的物体在这样的坐标系中匀速运动。这一特性使我们能够将惯性坐标系与任何其他坐标系区分开来。”

A body on which no external forces are acting moves uniformly in such a C.S. This property thus enables us to distinguish an inertial C.S. from any other.”

“但是，说没有力作用于物体究竟是什么意思呢？”

“ But what does it mean to say that no forces are acting on a body?”

“它只是意味着物体在惯性坐标系中均匀运动”

“ It simply means that the body moves uniformly in an inertial C.S.”

这里我们可以再次提出这个问题：“什么是惯性坐标系？”但是由于获得与上述不同的答案的希望很小，因此让我们尝试通过改变问题来获取一些具体的信息：

Here we could once more put the question: “ What is an inertial C.S.? ” But since there is little hope o f obtaining an answer differing from the above, let us try to gain some concrete information by changing the question:

“ 与地球刚性连接的 CS 是否是 e 上的惯性？”

“ Is a C.S. rigidly connected with the earth an inertial on e?”

“不，因为地球自转，力学定律在地球上并不严格有效。CS

“ N o, because the laws o f mechanics are not rigorously valid on the earth, due to its rotation. A C.S.

与太阳刚性连接的物体在许多问题中可以看作惯性坐标系；但是当我们谈论旋转的太阳时，我们又明白坐标系

rigidly connected with the sun can be regarded for many problems as an inertial C.S.; but when we speak o f the rotating sun, we again understand that a C.S.

与之相关的不能被视为严格的惯性。”

connected with it cannot be regarded as strictly inertial.”

“那么，你的惯性坐标系具体是什么，它的运动状态如何选择？”

“ Then what, concretely, is your inertial C.S., and how is its state o f motion to be chosen?”

“这只是一个有用的虚构，我不知道如何实现它。如果我能远离所有物质身体，摆脱所有外界影响，那么我的 CS 就会是惯性的。”

“ It is merely a useful fiction and I have no idea how to realize it. I f I could only get far away from all material bodies and free myself from all external influences, my C.S. would then be inertial.”

“但是，你说的不受任何外界影响的 CS 是什么意思呢？”

“ But what do you mean by a C.S. free from all external influences?”

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“我的意思是 CS 是惯性的。”

“ I mean that the C.S. is inertial.”

我们再次回到最初的问题！

O nce more we are back at our initial question !

我们的采访揭示了古典物理学的一个重大难题。我们有定律，但不知道该用什么框架来引用它们，我们的整个物理结构似乎都建立在沙子上。

O u r interview reveals a grave difficulty in classical physics. We have laws, but do not know what frame to refer them to, and our whole physical structure seems to be built on sand.

我们可以从不同的角度来处理同样的难题。试想一下，在整个宇宙中只有一个物体构成我们的坐标系。这个物体开始旋转。根据经典力学，旋转物体的物理定律与非旋转物体的物理定律不同。如果惯性原理在一种情况下有效，那么在另一种情况下就无效。但这一切听起来都很可疑。在整个宇宙中只考虑一个物体的运动是可以的吗？

We can approach this same difficulty from a different point o f view. T ry to imagine that there is only one body, forming our C.S., in the entire universe. This body begins to rotate. According to classical mechanics, the physical laws for a rotating body are different from those for a non-rotating body. I f the inertial principle is valid in one case, it is not valid in the other. But all this sounds very suspicious. Is it permissible to consider the motion of only one body in the entire universe?

我们所说的物体的运动总是指其相对于另一个物体的位置变化。因此，只谈论一个物体的运动是违背常识的。经典力学和常识在这一点上存在着巨大的分歧。牛顿的方法是：如果惯性原理有效，那么 CS 要么处于静止状态，要么处于匀速运动状态。如果惯性原理无效，那么物体处于非匀速运动状态。

By the motion of a body we always mean its change of position in relation to a second body. It is, therefore, contrary to common sense to speak about the motion o f only one body. Classical mechanics and common sense disagree violently on this point. Newton’s recipe is: if the inertial principle is valid, then the C.S. is either at rest or in uniform motion. I f the inertial principle is invalid, then the body is in non-uniform motion.

因此，我们对运动或静止的判断取决于所有物理定律是否适用于给定的坐标系

Thus, our verdict of motion or rest depends upon whether or not all the physical laws are applicable to a given C.S.

以太阳和地球两个天体为例。

Take two bodies, the sun and the earth, for instance.

我们观察到的运动又是 相对的。它可以通过将坐标系与地球或太阳连接起来来描述。从这个角度来看，哥白尼的伟大

The motion we observe is again relative. It can be described by connecting the C.S. with either the earth or the sun. From this point of view, Copernicus’ great

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成就在于将坐标系从地球转移到太阳。但由于运动是相对的，而且可以使用任何参考系，因此似乎没有理由偏向某一坐标系而不偏向另一坐标系。

achievement lies in transferring the C.S. from the earth to the sun. But as motion is relative and any frame of reference can be used, there seems to be no reason for favouring one C.S. rather than the other.

物理学再次介入并改变了我们的常识观点。与太阳相连的坐标系比与地球相连的坐标系更像惯性系统。物理定律应该适用于哥白尼的坐标系而不是托勒密的坐标系。只有从物理学的角度才能体会到哥白尼发现的伟大之处。它说明了使用与太阳刚性相连的坐标系来描述行星运动的巨大优势。

Physics again intervenes and changes our common-sense point of view. The C.S. connected with the sun resembles an inertial system more than that connected with the earth. The physical laws should be applied to Copernicus’ C.S. rather than to Ptolemy’s. The greatness of Copernicus’ discovery can be appreciated only from the physical point of view. It illustrates the great advantage of using a C.S. connected rigidly with the sun for describing the motion of planets.

经典物理学中不存在绝对的匀速运动。

No absolute uniform motion exists in classical physics.

如果两个坐标系相对于彼此做匀速运动，那么说“这个坐标系静止，另一个坐标系运动”就没有意义了。但是，如果两个坐标系相对于彼此做非匀速运动，那么就有很好的理由说“这个物体运动，另一个物体静止（或匀速运动）”。绝对运动在这里具有非常明确的含义。在这一点上，常识和经典物理学之间存在着巨大的鸿沟。所提到的困难，即惯性系的困难和绝对运动的困难，是紧密相连的。绝对运动只有通过惯性系的概念才有可能，自然定律对惯性系有效。

I f two C.S. are moving uniformly, relative to each other, then there is no sense in saying, “ This C.S. is at rest and the other is m oving” . But if two C.S. are moving non-uniformly, relative to each other, then there is very good reason for saying, “ This body moves and the other is at rest (or moves uniformly) ” . Absolute motion has here a very definite meaning. There is, at this point, a wide gulf between common sense and classical physics. The difficulties mentioned, that of an inertial system and that of absolute motion, are strictly connected with each other. Absolute motion is made possible only by the idea of an inertial system, for which the laws of nature are valid.

看起来这些困难似乎无路可走，似乎没有物理理论可以避免它们。它们的根源在于自然法则的有效性

It may seem as though there is no way out of these difficulties, as though no physical theory can avoid them. Their root lies in the validity of the laws of nature

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只适用于一类特殊的 CS，即惯性。解决这些困难的可能性取决于对以下问题的回答。我们能否制定物理定律，使它们对所有 CS 都有效，不仅是那些匀速运动的 CS，而且还有那些相对彼此任意运动的 CS？如果能做到这一点，我们的困难就解决了。然后我们就能把自然定律应用于任何 CS。科学早期托勒密和哥白尼观点之间的激烈斗争将变得毫无意义。两种 CS 都可以同等合理地使用。

for a special class of C.S. only, the inertial. The possibility o f solving these difficulties depends on the answer to the following question. C an we formulate physical laws so that they are valid for all C.S., not only those moving uniformly, but also those moving quite arbitrarily, relative to each other? I f this can be done, our difficulties will be over. We shall then be able to apply the laws o f nature to any C.S. The struggle, so violent in the early days of science, between the views o f Ptolemy and Copernicus would then be quite meaningless. Either C.S. could be used with equal justification.

“太阳静止而地球运动”或“太阳运动而地球静止”这两句话只是意味着涉及两个不同CS的两个不同约定

The two sentences, “ the sun is at rest and the earth moves” , or “ the sun moves and the earth is at rest” , would simply mean two different conventions concerning two different C.S.

我们能否建立一个适用于所有 CS 的真实相对论物理学？一个没有绝对运动、只有相对运动的物理学？这确实是可能的！

Could we build a real relativistic physics valid in all C.S.; a physics in which there would be no place for absolute, but only for relative, motion? This is indeed possible!

我们至少有一个迹象，尽管这个迹象非常微弱，表明如何构建新物理学。真正的相对论物理学必须适用于所有 CS，因此也适用于惯性 CS 的特殊情况。我们已经知道此惯性 CS 的定律。在惯性系统的特殊情况下，适用于所有 CS 的新一般定律必须归结为旧的已知定律。

We have at least one indication, though a very weak one, of how to build the new physics. Really relativistic physics must apply to all C.S. and, therefore, also to the special case of the inertial C.S. We already know the laws for this inertial C.S. The new general laws valid for all C.S. must, in the special case of the inertial system, reduce to the old, known laws.

广义相对论解决了为每一个坐标系制定物理定律的问题；而之前的理论只适用于惯性系，被称为 狭义相对论。这两个理论

The problem of formulating physical laws for every C.S. was solved by the so-called general relativity theory; the previous theory, applying only to inertial systems, is called the special relativity theory. The two theories

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当然，它们不能相互矛盾，因为我们必须始终将狭义相对论的旧定律纳入惯性系的一般定律中。但正如惯性坐标系以前是唯一一个物理定律得以制定的坐标系一样，现在它将形成特殊的极限情况，因为所有相对彼此任意移动的坐标系都是允许的。

cannot, o f course, contradict each other, since we must always include the old laws of the special relativity theory in the general laws for an inertial system. But just as the inertial C.S. was previously the only one for which physical laws were formulated, so now it will form the special limiting case, as all C.S. moving arbitrarily, relative to each other, are permissible.

这是广义相对论的纲领。但在勾勒出它实现的方式时，我们必须比迄今为止更加模糊。科学发展中出现的新困难迫使我们的理论变得越来越抽象。意想不到的冒险仍在等待我们。但我们的最终目标始终是更好地理解现实。

This is the programme for the general theory of relativity. But in sketching the way in which it was accomplished we must be even vaguer than we have been so far. New difficulties arising in the development of science force our theory to become more and more abstract. Unexpected adventures still await us. But our final aim is always a better understanding of reality.

连接理论和观察的逻辑链中不断增加环节。为了清除从理论到实验的不必要的人为假设，以涵盖更广泛的事实领域，我们必须使这条链越来越长。我们的假设越简单、越基本，我们的数学推理工具就越复杂；从理论到观察的道路就越长、越微妙、越复杂。虽然这听起来很矛盾，但我们可以说：现代物理学比旧物理学更简单，因此似乎更困难、更复杂。我们对外部世界的描绘越简单，它所包含的事实越多，它在我们的头脑中反映宇宙的和谐就越强烈。

Links are added to the chain of logic connecting theory and observation. To clear the way leading from theory to experiment of unnecessary and artificial assumptions, to embrace an ever-wider region of facts, we must make the chain longer and longer. The simpler and more fundamental our assumptions become, the more intricate is our mathematical tool of reasoning; the way from theory to observation becomes longer, more subtle, and more complicated. Although it sounds paradoxical, we could say: Modern physics is simpler than the old physics and seems, therefore, more difficult and intricate. The simpler our picture of the external world and the more facts it embraces, the more strongly it reflects in our minds the harmony of the universe.

我们的新想法很简单：建立一个适用于EE的物理学

O ur new idea is simple: to build a physics valid for E E

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所有 CS 它的实现带来了形式上的复杂性，迫使我们使用与迄今为止物理学中使用的不同的数学工具。我们在这里只展示这个计划的实现与两个主要问题之间的联系：引力和几何学。

all C.S. Its fulfilment brings formal complications and forces us to use mathematical tools different from those so far employed in physics. We shall show here only the connection between the fulfilment of this programme and two principal problems: gravitation and geometry.

出局 ID EAND 入局 S ID ETHEL IF T

O U T S ID E A N D IN S ID E T H E L IF T

惯性定律标志着物理学的第一个重大进步；事实上，这是物理学真正的开端。它是通过对理想化实验的思考而获得的，即一个物体永远运动，没有摩擦，也没有任何其他外力作用。从这个例子，以及后来的许多其他例子中，我们认识到了由思想创造的理想化实验的重要性。这里再次讨论理想化实验。虽然这些听起来可能非常奇妙，但它们将帮助我们通过简单的方法尽可能多地了解相对论。

The law of inertia marks the first great advance in physics; in fact, its real beginning. It was gained by the contemplation of an idealized experiment, a body moving forever with no friction nor any other external forces acting. From this example, and later from many others, we recognized the importance of the idealized experiment created by thought. Here again, idealized experiments will be discussed. Although these may sound very fantastic, they will, nevertheless, help us to understand as much about relativity as is possible by our simple methods.

我们之前做过理想化的实验，实验对象是匀速移动的房间。这次，我们换一种方式，实验对象是下降的电梯。

We had previously the idealized experiments with a uniformly moving room. Here, for a change, we shall have a falling lift.

想象一下，在摩天大楼的顶部有一个比任何实际建筑都高得多的大型电梯。突然，支撑电梯的电缆断裂，电梯自由落向地面。电梯中的观察者在坠落过程中进行实验。在描述它们时，我们不必担心空气阻力或摩擦力，因为我们可以在理想条件下忽略它们的存在。其中一名观察者从口袋里掏出手帕和手表，然后掉落

Imagine a great lift at the top of a skyscraper much higher than any real one. Suddenly the cable supporting the lift breaks, and the lift falls freely toward the ground. Observers in the lift are performing experiments during the fall. In describing them, we need not bother about air resistance or friction, for we may disregard their existence under our idealized conditions. One of the observers takes a handkerchief and a watch from his pocket and drops

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它们。这两个物体会发生什么？对于从电梯窗户向外看的外部观察者来说，手帕和手表以完全相同的方式、相同的加速度向地面下落。我们记得，下落物体的加速度与其质量完全无关，正是这一事实揭示了引力质量和惯性质量的相等（第 37 页）。我们还记得，从经典力学的角度来看，引力质量和惯性质量相等是完全偶然的，在其结构中不起作用。然而，在这里，这种反映在所有下落物体的相等加速度中的相等是至关重要的，并构成了我们整个论证的基础。

them. What happens to these two bodies? For the outside observer, who is looking through the window of the lift, both handkerchief and watch fall toward the ground in exactly the same way, with the same acceleration. We remember that the acceleration of a falling body is quite independent of its mass and that it was this fact which revealed the equality o f gravitational and inertial mass (p. 37). We also remember that the equality o f the two masses, gravitational and inertial, was quite accidental from the point of view of classical mechanics and played no role in its structure. Here, however, this equality reflected in the equal acceleration of all falling bodies is essential and forms the basis of our whole argument.

让我们回到下落的手帕，观察一下；对于外部观察者来说，它们都以相同的加速度下落。但电梯也是如此，有墙壁、天花板和地板。因此：两个物体与地板之间的距离不会改变。对于内部观察者来说，两个物体仍然保持他放手时的位置。内部观察者可以忽略引力场，因为引力场的来源位于他的坐标系之外。他发现电梯内没有任何力作用在这两个物体上，所以它们处于静止状态，就像它们处于惯性坐标系中一样。电梯里发生了奇怪的事情！如果观察者将物体推向任何方向，例如向上或向下，只要它不与电梯的天花板或地板相撞，它总是均匀移动。简而言之，经典力学定律对观察者有效

Let us return to our falling handkerchief and watch; for the outside observer they are both falling with the same acceleration. But so is the lift, with its walls, ceiling, and floor. Therefore: the distance between the two bodies and the floor will not change. For the inside observer the two bodies remain exactly where they were when he let them go. The inside observer may ignore the gravitational field, since its source lies outside his C.S. H e finds that no forces inside the lift act upon the two bodies, and so they are at rest, just as if they were in an inertial C.S. Strange things happen in the lift ! I f the observer pushes a body in any direction, up or down for instance, it always moves uniformly so long as it does not collide with the ceiling or the floor of the lift. Briefly speaking, the laws o f classical mechanics are valid for the observer

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升降机内部。所有物体的行为都符合惯性定律。我们与自由落体升降机刚性连接的新坐标系仅在一个方面与惯性坐标系不同。在惯性坐标系中，没有力作用的运动物体将永远匀速运动。经典物理学中表示的惯性坐标系不受空间和时间的限制。

inside the lift. A ll bodies behave in the way expected by the law of inertia. O ur new C.S. rigidly connected with the freely falling lift differs from the inertial C.S. in only one respect. In an inertial C.S., a moving body on which no forces are acting will move uniformly for ever. The inertial C.S. as represented in classical physics is neither limited in space nor time.

然而，我们电梯中的观察者的情况则不同。他的坐标系的惯性特征在空间和时间上是有限的。匀速运动的物体迟早会与电梯壁相撞，破坏匀速运动。迟早整个电梯会与地球相撞，摧毁观察者和他们的实验。坐标系只是一个

The case of the observer in our lift is, however, different. The inertial character of his C.S. is limited in space and time. Sooner or later the uniformly moving body will collide with the wall of the lift, destroying the uniform motion. Sooner or later the whole lift will collide with the earth, destroying the observers and their experiments. The C.S. is only a

真实惯性坐标系的“袖珍版”

“ pocket edition” of a real inertial C.S.

坐标系的这种局部特性非常重要。如果我们想象中的升力从北极到达赤道，手帕放在北极，手表放在赤道上，那么对于外部观察者来说，这两个物体的加速度不会相同；它们不会相对于彼此静止。我们的整个论证将失败！升力的尺寸必须受到限制，以便可以假设所有物体相对于外部观察者的加速度相等。

This local character of the C.S. is quite essential. I f our imaginary lift were to reach from the North Pole to the Equator, with the handkerchief placed over the North Pole and the watch over the Equator, then, for the outside observer, the two bodies would not have the same acceleration; they would not be at rest relative to each other. O ur whole argument would fa il! The dimensions of the lift must be limited so that the equality of acceleration of all bodies relative to the outside observer may be assumed.

有了这种限制，CS 对于内部观察者来说具有惯性特征。我们至少可以指出一个所有物理定律都有效的 CS，即使它在时间和空间上受到限制。如果我们想象另一个 CS，另一个升降机相对于

With this restriction, the C.S. takes on an inertial character for the inside observer. We can at least indicate a C.S. in which all the physical laws are valid, even though it is limited in time and space. I f we imagine another C.S., another lift moving uniformly, relative to

22C

一个自由落体，那么这两个坐标系都是局部惯性的。所有定律在两个坐标系中完全相同。从一个坐标系到另一个坐标系的转换由洛伦兹变换给出。

the one falling freely, then both these C.S. will be locally inertial. A ll laws are exactly the same in both. The transition from one to the other is given by the Lorentz transformation.

让我们看看电梯内外的观察者如何描述电梯内发生的事情。

Let us see in what way both the observers, outside and inside, describe what takes place in the lift.

外部观察者注意到升降机和升降机内所有物体的运动，发现它们符合牛顿引力定律。对他来说，由于地球引力场的作用，运动不是匀速的，而是加速的。

The outside observer notices the motion of the lift and of all bodies in the lift, and finds them in agreement with Newton’s gravitational law. For him, the motion is not uniform, but accelerated, because of the action of the gravitational field of the earth.

然而，在电梯里出生和长大的一代物理学家却有着截然不同的看法。

However, a generation of physicists born and brought up in the lift would reason quite differently.

他们会相信自己拥有一个惯性系统，并且会将所有自然定律都归结于他们的升力，并有理有据地指出，这些定律在他们的坐标系中呈现出一种特别简单的形式。他们会很自然地假设他们的升力处于静止状态，他们的坐标系是惯性坐标系。

They would believe themselves in possession o f an inertial system and would refer all laws o f nature to their lift, stating with justification that the laws take on a specially simple form in their C.S. It would be natural for them to assume their lift at rest and their C.S. the inertial one.

不可能解决外部观察者和内部观察者之间的分歧。他们每个人都可以声称有权将所有事件归咎于他的 CS。两种事件的描述都可以同样一致。

It is impossible to settle the differences between the outside and the inside observers. Each of them could claim the right to refer all events to his C.S. Both descriptions of events could be made equally consistent.

我们从这个例子中看到，即使两个不同的坐标系相对运动不均匀，对物理现象的描述也是一致的。但对于这样的描述，我们必须考虑引力，也就是建立“桥梁”

We see from this example that a consistent description of physical phenomena in two different C.S. is possible, even if they are not moving uniformly, relative to each other. But for such a description we must take into account gravitation, building, so to speak, the “ bridge”

这会导致从一个 CS 到另一个 CS 的转变。

which effects a transition from one C.S. to the other.

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对于外部观察者来说，引力场是存在的；对于内部观察者来说，引力场是不存在的。对于外部观察者来说，重力场中的升力是加速运动，而对于内部观察者来说，重力场是静止的，不存在的。但是，使两种坐标系中的描述成为可能的“桥梁”——引力场，依赖于一个非常重要的支柱：引力质量和惯性质量的等价性。如果没有这个在经典力学中被忽视的线索，我们目前的论证将完全失败。

The gravitational field exists for the outside observer; it does not for the inside observer. Accelerated motion of the lift in the gravitational field exists for the outside observer, rest and absence of the gravitational field for the inside observer. But the “ bridge” , the gravitational field, making the description in both C.S. possible, rests on one very important pillar: the equivalence of gravitational and inertial mass. Without this clue, unnoticed in classical mechanics, our present argument would fail completely.

现在进行一个略有不同的理想化实验。

Now for a somewhat different idealized experiment.

假设存在一个惯性坐标系，惯性定律在其中有效。我们已经描述了在这种惯性坐标系中静止的升降机会发生什么情况

There is, let us assume, an inertial C.S., in which the law of inertia is valid. We have already described what happens in a lift resting in such an inertial C.S.

但现在我们换个角度看。外面有人把绳子系在电梯上，用恒定的力拉着，朝着我们画的方向——

But we now change our picture. Someone outside has fastened a rope to the lift and is pulling, with a constant force, in the direction indicated in our draw-

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ing。如何做到这一点并不重要。由于力学定律在此 CS 中有效，因此整个升降机以恒定加速度沿运动方向移动。我们将再次听取外部和内部观察者对升降机中发生的现象的解释。

ing. It is immaterial how this is done. Since the laws of mechanics are valid in this C.S., the whole lift moves with a constant acceleration in the direction of the motion. Again we shall listen to the explanation of phenomena going on in the lift and given by both the outside and inside observers.

外部观察者： 我的坐标系是惯性坐标系。电梯以恒定加速度移动，因为有恒定的力在作用。电梯内的观察者处于绝对运动状态，对他们来说，力学定律是无效的。他们发现没有力作用的物体是静止的。如果物体自由移动，它很快就会与电梯的地板相撞，因为地板会向上朝着物体移动。手表和手帕的情况完全一样。我觉得很奇怪，电梯内的观察者必须始终在“地板”上，因为只要他跳起来，地板就会再次到达他。

The outside observer: M y C.S. is an inertial one. The lift moves with constant acceleration, because a constant force is acting. The observers inside are in absolute motion, for them the laws of mechanics are invalid. They do not find that bodies, on which no forces are acting, are at rest. I f a body is left free, it soon collides with the floor of the lift, since the floor moves upward toward the body. This happens exactly in the same way for a watch and for a handkerchief. It seems very strange to me that the observer inside the lift must always be on the “ floor” , because as soon as he jumps the floor will reach him again.

内部观察者： 我看不出有任何理由相信我的升降机处于绝对运动中。我同意我的 CS 与升降机刚性连接，并不是真正的惯性，但我不相信它与绝对运动有任何关系。我的手表、手帕和所有物体都在下落，因为整个升降机都在引力场中。我注意到的运动与地球上的人完全相同。他用引力场的作用非常简单地解释了它们。对我来说也是如此。

The inside observer: I do not see any reason for believing that my lift is in absolute motion. I agree that my C.S., rigidly connected with my lift, is not really inertial, but I do not believe that it has anything to do with absolute motion. M y watch, my handkerchief, and all bodies are falling because the whole lift is in a gravitational field. I notice exactly the same kinds o f motion as the man on the earth. H e explains them very simply by the action o f a gravitational field. The same holds good for me.

这两种描述，一种是外部的，另一种是

These two descriptions, one by the outside, the other

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内部观察者的观点是完全一致的，无法确定哪一种是正确的。我们可以假设其中一种来描述电梯中的现象：外部观察者的运动不均匀且没有引力场，内部观察者的运动静止且有引力场。

by the inside, observer, are quite consistent, and there is no possibility of deciding which of them is right. We may assume either one o f them for the description of phenomena in the lift: either non-uniform motion and absence of a gravitational field with the outside observer, or rest and the presence of a gravitational field with the inside observer.

外部观察者可能会认为升力是“绝对”的非匀速运动。但是，如果运动被假设为存在引力场，那么它就不能被视为绝对运动。

The outside observer may assume that the lift is in “ absolute” non-uniform motion. But a motion which is wiped out by the assumption of an acting gravitational field cannot be regarded as absolute motion.

或许，有一种方法可以解决两种不同描述的歧义问题，也许可以做出支持其中一种而不是另一种的决定。想象一下，一束光线从侧窗水平进入电梯，并在很短的时间后到达对面的墙壁。让我们再看看两位观察者如何预测光的路径。

There is, possibly, a way out of the ambiguity of two such different descriptions, and a decision in favour of one against the other could perhaps be made. Imagine that a light ray enters the lift horizontally through a side window and reaches the opposite wall after a very short time. Again let us see how the path of the light would be predicted by the two observers.

外部观察者相信电梯在加速运动，他们会说：光线进入窗户，沿着直线以恒定速度水平向对面的墙壁移动。但电梯向上移动，在光线向墙壁传播的过程中，电梯会改变位置。因此，光线会相遇的地方不是正好在入口点的对面，而是在入口点稍下方。差别很小，但确实存在，光线相对于电梯不是沿着直线传播，而是沿着略微倾斜的直线传播。

The outside observer, believing in accelerated motion o f the lift, would argue: The light ray enters the window and moves horizontally, along a straight line and with a constant velocity, toward the opposite wall. But the lift moves upward, and during the time in which the light travels toward the wall the lift changes its position. Therefore, the ray will meet at a point not exactly opposite its point of entrance, but a little below. The difference will be very slight, but it exists nevertheless, and the light ray travels, relative to the lift, not along a straight, but along a slightly

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曲线。差异是由于射线穿过内部时升力所覆盖的距离造成的。

curved line. The difference is due to the distance covered by the lift during the time the ray is crossing the interior.

内部观察者相信重力场作用于电梯内的所有物体，他会说：电梯没有加速运动，只有重力场的作用。光束没有重量，因此不会受到重力场的影响。如果以水平方向发送，它将在与进入点完全相反的位置与墙壁相遇。

The inside observer, who believes in the gravitational field acting on all objects in his lift, would say: there is no accelerated motion of the lift, but only the action of the gravitational field. A beam of light is weightless and, therefore, will not be affected by the gravitational field. I f sent in a horizontal direction, it will meet the wall at a point exactly opposite to that at which it entered.

从这个讨论来看，似乎有可能在两种相反的观点之间做出决定，因为对于两个观察者来说，现象是不同的。如果刚才引用的两种解释都没有什么不合逻辑的地方，那么我们之前的整个论点就被推翻了，我们无法用两种一致的方式来描述所有现象，即有引力场和没有引力场。

It seems from this discussion that there is a possibility of deciding between these two opposite points of view as the phenomenon would be different for the two observers. I f there is nothing illogical in either of the explanations just quoted, then our whole previous argument is destroyed, and we cannot describe all phenomena in two consistent ways, with and without a gravitational field.

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但幸运的是，内部观察者的推理有一个严重错误，这挽救了我们先前的结论。他说：“一束光没有重量，因此不会受到引力场的影响。”这不可能是对的！一束光携带能量，能量有质量。但每个惯性质量都会被引力场吸引，因为惯性质量和引力质量是相等的。一束光在引力场中的弯曲程度，恰好与以等于光速的速度水平抛出的物体的弯曲程度相同。如果内部观察者的推理正确，并考虑到光线在引力场中的弯曲，那么他的结果将与外部观察者的结果完全相同。

But there is, fortunately, a grave fault in the reasoning o f the inside observer, which saves our previous conclusion. H e said: “ A beam of light is weightless and, therefore, will not be affected by the gravitational field.” This cannot be r ig h t! A beam of light carries energy and energy has mass. But every inertial mass is attracted by the gravitational field, as inertial and gravitational masses are equivalent. A beam of light will bend in a gravitational field exactly as a body would if thrown horizontally with a velocity equal to that of light. I f the inside observer had reasoned correctly and had taken into account the bending of light rays in a gravitational field, then his results would have been exactly the same as those o f an outside observer.

当然，地球引力场太弱，光线在其中发生弯曲无法通过实验直接证明。但在日食期间进行的著名实验虽然间接但确凿地表明了引力场对光线路径的影响。

The gravitational field o f the earth is, of course, too weak for the bending o f light rays in it to be proved directly, by experiment. But the famous experiments performed during the solar eclipses show, conclusively though indirectly, the influence o f a gravitational field on the path o f a light ray.

从这些例子可以看出，我们有充分的理由希望建立相对论物理学。但为此，我们必须首先解决引力问题。

It follows from these examples that there is a well-founded hope o f formulating a relativistic physics. But for this we must first tackle the problem of gravitation.

我们从升力的例子中看到了两种描述的一致性。非均匀运动可以假设，也可以不假设。我们可以消除“绝对”

We saw from the example of the lift the consistency of the two descriptions. Non-uniform motion may, or may not, be assumed. We can eliminate “ absolute”

从我们的例子可以看出，重力场会引起运动。

motion from our examples by a gravitational field.

但非匀速运动却没有绝对的东西，引力场可以把它完全消灭。

But then there is nothing absolute in the non-uniform motion. The gravitational field is able to wipe it out completely.

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绝对运动和惯性坐标系的幽灵可以从物理学中被驱除，并建立一种新的相对论物理学。我们的理想化实验表明广义相对论问题与引力问题密切相关，以及引力质量和惯性质量的等价性对于这种联系如此重要。显然，广义相对论中引力问题的解法必须不同于牛顿解法。引力定律必须像所有自然定律一样，针对所有可能的坐标系制定，而牛顿制定的经典力学定律仅在惯性坐标系中有效

The ghosts of absolute motion and inertial C.S. can be expelled from physics and a new relativistic physics built. O ur idealized experiments show how the problem of the general relativity theory is closely connected with that o f gravitation and why the equivalence of gravitational and inertial mass is so essential for this connection. It is clear that the solution of the gravitational problem in the general theory of relativity must differ from the Newtonian one. The laws of gravitation must, just as all laws of nature, be formulated for all possible C.S., whereas the laws of classical mechanics, as formulated by Newton, are valid only in inertial C.S.

几何与实验

G E O M E T R Y A N D E X P E R I M E N T

我们的下一个例子将比升降机坠落的例子更加奇妙。我们必须着手解决一个新问题，即广义相对论与几何学之间的联系。让我们从描述一个只有二维生物而不是三维生物（就像我们这个世界一样）的世界开始。电影已经让我们习惯了二维生物在二维屏幕上的表演。现在让我们想象一下，这些影子人物，也就是屏幕上的演员，确实存在，他们有思考的能力，他们可以创造自己的科学，对他们来说，二维屏幕代表几何空间。这些生物无法具体地想象三维空间，就像我们无法想象一个三维世界一样。

O ur next example will be even more fantastic than the one with the falling lift. We have to approach a new problem; that o f a connection between the general relativity theory and geometry. Let us begin with the description of a world in which only two-dimensional and not, as in ours, three-dimensional creatures live. The cinema has accustomed us to two-dimensional creatures acting on a two-dimensional screen. Now let us imagine that these shadow figures, that is, the actors on the screen, really do exist, that they have the power of thought, that they can create their own science, that for them a two-dimensional screen stands for geometrical space. These creatures are unable to imagine, in a concrete way, a three-dimensional space just as we are unable to imagine a world of

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四维空间。他们可以偏转直线；他们知道什么是圆，但他们无法构造球体，因为这意味着要放弃他们的二维屏幕。我们的情况也类似。我们能够偏转和弯曲线和面，但我们几乎无法想象一个偏转和弯曲的三维空间。

four dimensions. They can deflect a straight line; they know what a circle is, but they are unable to construct a sphere, because this would mean forsaking their two-dimensional screen. We are in a similar position. We are able to deflect and curve lines and surfaces, but we can scarcely picture a deflected and curved three-dimensional space.

通过生活、思考和实验，我们的影子人物最终能够掌握二维欧几里得几何的知识。因此，他们可以证明，例如，三角形内角和为 180 度。他们可以构造两个有共同圆心的圆，一个很小，另一个很大。

By living, thinking, and experimenting, our shadow figures could eventually master the knowledge o f the two-dimensional Euclidean geometry. Thus, they could prove, for example, that the sum o f the angles in a triangle is 180 degrees. They could construct two circles with a common centre, one very small, the other large.

他们会发现，两个圆的周长之比等于半径之比，这也是欧几里得几何学的一个特征。如果屏幕无限大，这些影子生物就会发现，一旦他们开始直线旅行，就再也不会回到出发点了。

They would find that the ratio of the circumferences of two such circles is equal to the ratio of their radii, a result again characteristic of Euclidean geometry. I f the screen were infinitely great, these shadow beings would find that once having started a journey straight ahead, they would never return to their point of departure.

现在让我们想象一下这些二维生物生活在变化的环境中。让我们想象一下，有人从外部，即“第三维度”，将它们从屏幕转移到一个半径很大的球体表面。如果这些阴影相对于整个表面来说非常小，如果它们没有远程通信手段，也不能移动很远，那么它们就不会意识到任何变化。小三角形的角度总和仍然等于 180 度。两个有共同中心的小圆圈仍然表明

Let us now imagine these two-dimensional creatures living in changed conditions. Let us imagine that someone from the outside, the “ third dimension” , transfers them from the screen to the surface of a sphere with a very great radius. I f these shadows are very small in relation to the whole surface, if they have no means of distant communication and cannot move very far, then they will not be aware of any change. The sum of angles in small triangles still amounts to 180 degrees. Two small circles with a common centre still show that the

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它们的半径与圆周的比相等。沿直线的旅程永远不会让他们回到起点。

ratio of their radii and circumferences are equal. A journey along a straight line never leads them back to the starting-point.

但随着时间的推移，让这些影子生物发展他们的理论和技术知识。让他们找到能够迅速覆盖大距离的通讯手段。然后他们会发现，从直线前进的旅程开始，他们最终会回到出发点。“直线前进”意味着沿着球体的大圆前进。

But let these shadow beings, in the course of time, develop their theoretical and technical knowledge. Let them find means of communication which will enable them to cover large distances swiftly. They will then find that starting on a journey straight ahead, they ultimately return to their point of departure. “ Straight ahead” means along the great circle of the sphere.

他们还会发现，如果两个具有共同圆心的圆中的一个半径较小而另一个半径较大，则它们的比值不等于半径的比值。

They will also find that the ratio of two circles with a common centre is not equal to the ratio of the radii, if one of the radii is small and the other great.

如果我们的二维生物是保守的，如果他们在过去几代人无法远行时就学会了欧几里得几何，而且这种几何与观察到的事实相符，那么他们肯定会尽一切可能坚持下去，尽管有测量的证据。他们可以尝试让物理学承担这些差异的负担。他们可以寻找一些物理原因，比如温度差异，使线条变形并导致偏离欧几里得几何。但是，迟早，他们必须发现有一种更合乎逻辑和令人信服的方式来描述这些事件。他们最终会明白，他们的世界是一个有限的世界，有着与他们学到的几何原理不同的几何原理。他们会明白，尽管他们无法想象，但他们的世界是一个球体的二维表面。他们

I f our two-dimensional creatures are conservative, if they have learned the Euclidean geometry for generations past when they could not travel far and when this geometry fitted the facts observed, they will certainly make every possible effort to hold on to it, despite the evidence o f their measurements. They could try to make physics bear the burden of these discrepancies. They could seek some physical reasons, say temperature differences, deforming the lines and causing deviation from Euclidean geometry. But, sooner or later, they must find out that there is a much more logical and convincing way of describing these occurrences. They will eventually understand that their world is a finite one, with different geometrical principles from those they learned. They will understand that, in spite of their inability to imagine it, their world is the two-dimensional surface of a sphere. They

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很快会学到新的几何原理，虽然这些原理与欧几里得几何不同，但同样可以以一致和合乎逻辑的方式为他们的二维世界制定。对于在球体几何知识的熏陶下成长起来的新一代人来说，旧的欧几里得几何会显得更加复杂和不自然，因为它不符合观察到的事实。

will soon learn new principles of geometry, which though differing from the Euclidean can, nevertheless, be formulated in an equally consistent and logical way for their two-dimensional world. For the new generation brought up with a knowledge o f the geometry of the sphere, the old Euclidean geometry will seem more complicated and artificial since it does not fit the facts observed.

让我们回到我们这个世界的三维生物。

Let us return to the three-dimensional creatures of our world.

我们的三维空间具有欧几里得特征这一说法是什么意思呢？其含义是，欧几里得几何中所有逻辑上证明的陈述都可以用实际实验来证实。我们可以借助刚体或光线构造出与欧几里得几何的理想化对象相对应的对象。尺子的边缘或光线对应于直线；由细刚性杆构成的三角形的三个角之和为 180

What is meant by the statement that our three-dimensional space has a Euclidean character? The meaning is that all logically proved statements of the Euclidean geometry can also be confirmed by actual experiment. We can, with the help o f rigid bodies or light rays, construct objects corresponding to the idealized objects o f Euclidean geometry. The edge of a ruler or a light ray corresponds to the line; the sum of the angles o f a triangle built of thin rigid rods is 180

度；用细的不可弯曲的金属线制成的两个圆的半径之比等于它们的周长之比。这样解释，欧几里得几何就成了物理学的一个篇章，尽管是一个非常简单的篇章。

degrees; the ratio o f the radii o f two circles with a common centre constructed from thin unbendable wire is equal to that of their circumference. Interpreted in this way, the Euclidean geometry becomes a chapter of physics, though a very simple one.

但我们可以想象，人们已经发现了一些差异：例如，一个由杆构成的大三角形，由于许多原因必须被视为刚性的，其角度之和不是 180 度。

But we can imagine that discrepancies have been discovered: for instance, that the sum o f the angles o f a large triangle constructed from rods, which for many reasons had to be regarded as rigid, is not 180 degrees.

由于我们已经习惯了欧几里得几何对象的具体表示的思想

Since we are already used to the idea o f the concrete representation o f the objects o f Euclidean geometry

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刚体，我们可能应该寻找某种物理力作为杆的这种意外异常行为的原因。我们应该努力找到这种力的物理性质及其对其他现象的影响。为了挽救欧几里得几何，我们应该指责物体不是刚性的，与欧几里得几何中的物体不完全对应。我们应该努力找到一种更好的物体表示方法，使物体的行为符合欧几里得几何的预期。然而，如果我们不能成功地将欧几里得几何和物理学结合成一幅简单而一致的图景，我们就必须放弃我们的空间是欧几里得的思想，并在关于我们空间的几何特征的更一般假设下寻找一幅更令人信服的现实图景。

by rigid bodies, we should probably seek some physical force as the cause of such unexpected misbehaviour of our rods. We should try to find the physical nature of this force and its influence on other phenomena. To save the Euclidean geometry, we should accuse the objects of not being rigid, of not exactly corresponding to those of Euclidean geometry. We should try to find a better representation o f bodies behaving in the way expected by Euclidean geometry. If, however, we should not succeed in combining Euclidean geometry and physics into a simple and consistent picture, we should have to give up the idea of our space being Euclidean and seek a more convincing picture o f reality under more general assumptions about the geometrical character of our space.

一个理想化的实验可以说明这种必要性，该实验表明真正的相对论物理学不能以欧几里得几何为基础。我们的论证将涉及惯性坐标系和狭义相对论的已知结果。

The necessity for this can be illustrated by an idealized experiment showing that a really relativistic physics cannot be based upon Euclidean geometry. O ur argument will imply results already learned about inertial C.S. and the special relativity theory.

想象一个大圆盘上画有两个圆圈，它们有共同的中心，一个圆圈非常小，另一个圆圈非常大。

Imagine a large disc with two circles with a common centre drawn on it, one very small, the other very large.

圆盘快速旋转。圆盘相对于外部观察者旋转，圆盘上有一个内部观察者。我们进一步假设外部观察者的坐标系是惯性坐标系。外部观察者可以在其惯性坐标系中绘制相同的两个圆圈，小圆圈和大圆圈，它们位于其坐标系中，但与旋转圆盘上的圆圈重合。欧几里得几何在他的坐标系中有效，因为它是惯性的，因此他将找到

The disc rotates quickly. The disc is rotating relative to an outside observer, and there is an inside observer on the disc. We further assume that the C.S. of the outside observer is an inertial one. The outside observer may draw, in his inertial C.S., the same two circles, small and large, resting in his C.S. but coinciding with the circles on the rotating disc. Euclidean geometry is valid in his C.S. since it is inertial, so that he will find the ratio of

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周长等于半径。但圆盘上的观察者又如何呢？从古典物理学和狭义相对论的角度来看，他的坐标系是禁忌的。但如果我们打算找到适用于任何坐标系的物理定律的新形式，那么我们必须以同样的严肃态度对待圆盘上的观察者和外面的观察者。我们现在从外面观察里面的观察者，看他如何通过测量找到旋转圆盘的周长和半径。他使用与外面观察者相同的小量尺。“相同”要么意味着真正相同，即由外面的观察者交给里面的观察者，要么意味着静止在坐标系中长度相同的两根量尺中的一根

the circumferences equal to that of the radii. But how about the observer on the disc? From the point of view of classical physics and also the special relativity theory, his C.S. is a forbidden one. But if we intend to find new forms for physical laws, valid in any C.S., then we must treat the observer on the disc and the observer outside with equal seriousness. W e, from the outside, are now watching the inside observer in his attempt to find, by measurement, the circumferences and radii on the rotating disc. H e uses the same small measuring stick used by the outside observer. “ The same” means either really the same, that is, handed by the outside observer to the inside, or, one of two sticks having the same length when at rest in a C.S.

圆盘内部的观察者开始测量

The inside observer on the disc begins measuring the

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小圆的半径和周长。他的结果必须与外部观察者的结果相同。圆盘旋转的轴线通过中心。

radius and circumference of the small circle. His result must be the same as that of the outside observer. The axis on which the disc rotates passes through the centre.

圆盘靠近中心的部分速度非常小。如果圆足够小，我们可以放心地应用经典力学，而忽略狭义相对论。这意味着对于外部和内部观察者来说，棍子的长度相同，并且这两个测量的结果对他们来说也相同。现在，圆盘上的观察者测量大圆的半径。对于外部观察者来说，棍子放在半径上会移动。然而，这样的棍子不会收缩，并且对于两个观察者来说长度相同，因为运动方向垂直于棍子。因此，对于两个观察者来说，三个测量值相同：两个半径和小圆周。但第四个测量值并非如此！对于两个观察者来说，大圆周的长度将不同。与静止的棍子相比，放在运动方向的圆周上的棍子现在对外部观察者来说似乎收缩了。速度比内圆的速度大得多，应该将这种收缩考虑在内。因此，如果我们应用狭义相对论的结果，我们的结论是：如果由两个观察者测量，大圆周的长度必定不同。由于两个观察者测量的四个长度中只有一个长度对他们来说不一样，因此两个半径的比率不可能等于

Those parts of the disc near the centre have very small velocities. I f the circle is small enough, we can safely apply classical mechanics and ignore the special relativity theory. This means that the stick has the same length for the outside and inside observers, and the result of these two measurements will be the same for them both. Now the observer on the disc measures the radius of the large circle. Placed on the radius, the stick moves, for the outside observer. Such a stick, however, does not contract and will have the same length for both observers, since the direction of the motion is perpendicular to the stick. Thus three measurements are the same for both observers: two radii and the small circumference. But it is not so with the fourth measurement! The length of the large circumference will be different for the two observers. The stick placed on the circumference in the direction of the motion will now appear contracted to the outside observer, compared to his resting stick. The velocity is much greater than that of the inner circle, and this contraction should be taken into account. If, therefore, we apply the results of the special relativity theory, our conclusion here is: the length of the great circumference must be different if measured by the two observers. Since only one o f the four lengths measured by the two observers is not the same for them both, the ratio of the two radii cannot be equal to the ratio of

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内部观察者的两个圆周与外部观察者的两个圆周相同。这意味着圆盘上的观察者无法确认欧几里得几何在他的 CS 中的有效性

the two circumferences for the inside observer as it is for the outside one. This means that the observer on the disc cannot confirm the validity of Euclidean geometry in his C.S.

在得到这个结果后，圆盘上的观察者可以说他不想考虑欧几里得几何无效的坐标系。欧几里得几何的失效是由于绝对旋转，是由于他的坐标系是一个糟糕的、被禁止的坐标系。但是，通过这种方式进行论证，他拒绝了广义相对论的主要思想。另一方面，如果我们想拒绝绝对运动并坚持广义相对论的思想，那么物理学就必须建立在比欧几里得几何更普遍的几何学的基础上。如果所有坐标系都是允许的，就无法摆脱这一后果。

After obtaining this result, the observer on the disc could say that he does not wish to consider C.S. in which Euclidean geometry is not valid. The breakdown of the Euclidean geometry is due to absolute rotation, to the fact that his C.S. is a bad and forbidden one. But, in arguing in this way, he rejects the principal idea of the general theory of relativity. O n the other hand, if we wish to reject absolute motion and to keep up the idea o f the general theory of relativity, then physics must all be built on the basis of a geometry more general than the Euclidean. There is no way of escape from this consequence if all C.S. are permissible.

广义相对论带来的变化不能只局限于空间。在狭义相对论中，我们让时钟静止在每个坐标系中，它们具有相同的节奏和同步，即同时显示相同的时间。非惯性坐标系中的时钟会发生什么情况？用圆盘进行的理想化实验将再次派上用场。外部观察者在其惯性坐标系中拥有完美的时钟，它们都具有相同的节奏，都是同步的。内部观察者拿两个相同类型的时钟，一个放在小内圈上，另一个放在大外圈上。内圈上的时钟相对于外部观察者的速度非常小。因此，我们可以有把握地得出结论，它的节奏将是

The changes brought about by the general relativity theory cannot be confined to space alone. In the special relativity theory we had clocks resting in every C.S., having the same rhythm and synchronized, that is, showing the same time simultaneously. What happens to a clock in a non-inertial C.S.? The idealized experiment with the disc will again be of use. The outside observer has in his inertial C.S. perfect clocks all having the same rhythm, all synchronized. The inside observer takes two clocks of the same kind and places one on the small inner circle and the other on the large outer circle. The clock on the inner circle has a very small velocity relative to the outside observer. We can, therefore, safely conclude that its rhythm will be the

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与外部时钟的相同。但是大圆上的时钟具有相当大的速度，与外部观察者的时钟相比，其节奏发生了变化，因此与放置在小圆上的时钟相比也是如此。因此，两个旋转的时钟将具有不同的节奏，并且应用狭义相对论的结果，我们再次看到，在我们的旋转 CS 中

same as that o f the outside clock. But the clock on the large circle has a considerable velocity, changing its rhythm compared to the clocks of the outside observer and, therefore, also compared to the clock placed on the small circle. Thus, the two rotating clocks will have different rhythms and, applying the results of the special relativity theory, we again see that in our rotating C.S.

我们不能做出类似于惯性坐标系中的安排

we can make no arrangements similar to those in an inertial C.S.

为了弄清楚从这个实验以及前面描述的理想化实验中可以得出什么结论，让我们再次引用相信古典物理学的老物理学家O和了解广义相对论的现代物理学家M之间的对话。

To make clear what conclusions can be drawn from this and previously described idealized experiments, let us once more quote a dialogue between the old physicist 0 , who believes in classical physics, and the modern physicist M , who knows the general relativity theory.

0 是外部观察者，位于惯性坐标系中，而M位于旋转的圆盘上。

0 is the outside observer, in the inertial C.S., whereas M is on the rotating disc.

0。在你的 CS 中，欧几里得几何无效。我看了你的测量结果，我同意在你的 CS 中，两个圆周的比率不等于两个半径的比率。但这表明你的 CS

0 . In your C.S., Euclidean geometry is not valid. I watched your measurements and I agree that the ratio o f the two circumferences is not, in your C.S., equal to the ratio o f the two radii. But this shows that your C.S.

是被禁止的。然而，我的坐标系具有惯性特征，因此我可以安全地应用欧几里得几何。

is a forbidden one. M y C.S., however, is o f an inertial character, and I can safely apply Euclidean geometry.

您的光盘处于绝对运动状态，并且从古典物理学的角度来看，形成了一个禁用 CS，其中力学定律无效。

Your disc is in absolute motion and, from the point of view of classical physics, forms a forbidden C.S., in which the laws of mechanics are not valid.

M 我不想听任何关于绝对运动的事情。我的 CS 和你的一样好。我注意到的是你相对于我的圆盘的旋转。没有人可以禁止我将所有运动与我的圆盘联系起来。

M . I do not want to hear anything about absolute motion. M y C.S. is just as good as yours. What I noticed was your rotation relative to my disc. No one can forbid me to relate all motions to my disc.

0 。但你没有感觉到一股奇怪的力量试图

0 . But did you not feel a strange force trying to

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让你远离圆盘中心？如果你的圆盘不是快速旋转的旋转木马，你观察到的两件事肯定不会发生。你不会注意到把你推向外面的力，也不会注意到欧几里得几何不适用于你的 CS 这些事实还不足以让你相信你的 CS 处于绝对运动中吗？

keep you away from the centre of the disc? I f your disc were not a rapidly rotating merry-go-round, the two things which you observed would certainly not have happened. You would not have noticed the force pushing you toward the outside nor would you have noticed that Euclidean geometry is not applicable in your C.S. Are not these facts sufficient to convince you that your C.S. is in absolute motion?

M。一点也不！我当然注意到了你提到的两个事实，但我认为作用在我圆盘上的一个奇怪的引力场是造成这两个事实的原因。引力场指向圆盘的外部，使我的刚性杆变形并改变我的时钟的节奏。对我来说，引力场、非欧几里得几何、具有不同节奏的时钟都紧密相连。接受任何 CS，我必须同时假设存在一个适当的引力场及其对刚性杆和时钟的影响。

M . Not at a l l ! I certainly noticed the two facts you mention, but I hold a strange gravitational field acting on my disc responsible for them both. The gravitational field, being directed toward the outside of the disc, deforms my rigid rods and changes the rhythm o f my clocks. The gravitational field, non-Euclidean geometry, clocks with different rhythms are, for me, all closely connected. Accepting any C.S., I must at the same time assume the existence of an appropriate gravitational field with its influence upon rigid rods and clocks.

0。但是，您是否意识到了您的广义相对论所造成的困难？我想举一个简单的非物理例子来阐明我的观点。

0 . But are you aware of the difficulties caused by your general relativity theory? I should like to make my point clear by taking a simple non-physical example.

想象一个理想化的美国小镇，它由平行的街道和与之垂直的平行大道组成。街道之间的距离和大道之间的距离始终相同。在这些假设成立的情况下，街区的大小完全相同。这样，我可以轻松描述任何街区的位置。但是，如果没有欧几里得几何学，这样的构造是不可能的。因此，对于

Imagine an idealized American town consisting of parallel streets with parallel avenues running perpendicular to them. The distance between the streets and also between the avenues is always the same. With these assumptions fulfilled, the blocks are o f exactly the same size. In this way I can easily characterize the position of any block. But such a construction would be impossible without Euclidean geometry. Thus, for

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例如，我们无法用一个伟大的美国理想城镇覆盖整个地球。看一眼地球仪你就会信服。但我们也无法用这样的“美国城镇建筑”覆盖你的圆盘。你声称你的杆因引力场而变形。

instance, we cannot cover our whole earth with one great ideal American town. One look at the globe will convince you. But neither could we cover your disc with such an “ American town construction” . You claim that your rods are deformed by the gravitational field.

你不能证实欧几里得关于半径和圆周率相等的定理，这一事实清楚地表明，如果你把这种街道和大道的构造进行得足够远，你迟早会陷入困境，发现在你的圆盘上是不可能的。你在旋转圆盘上的几何形状类似于曲面上的几何形状，当然，在曲面的很大一部分上不可能构造街道和大道。举一个更物理的例子，拿一个不规则加热的平面，表面的不同部分的温度不同。你能用小铁棒在温度升高时长度膨胀，实现“平行-垂直”

The fact that you could not confirm Euclid’s theorem about the equality o f the ratio of radii and circumferences shows clearly that if you carry such a construction of streets and avenues far enough you will, sooner or later, get into difficulties and find that it is impossible on your disc. Your geometry on your rotating disc resembles that on a curved surface, where, of course, the streets-and-avenues construction is impossible on a great enough part of the surface. For a more physical example take a plane irregularly heated with different temperatures on different parts of the surface. Can you, with small iron sticks expanding in length with temperature, carry out the “ parallel-perpendicular”

我在下面画的结构？当然不是！你的“引力场”也玩同样的把戏

construction which I have drawn below? O f course not! Your “ gravitational field” plays the same tricks

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随着小铁棒上温度的变化。

on your rods as the change of temperature on the small iron sticks.

M . 这一切并不让我害怕。街道的建设是为了确定点的位置，时钟是为了安排事件。城镇不一定是美国的，也可以是古老的欧洲。

M . A ll this does not frighten me. The street-avenue construction is needed to determine positions of points, with the clock to order events. The town need not be American, it could just as well be ancient European.

想象一下，你理想中的小镇是用橡皮泥做成的，然后变形了。我仍然可以给街区编号，认出街道和大道，尽管它们不再是笔直和等距的。同样，在我们的地球上，经度和纬度表示点的位置，尽管没有“美国小镇”的建筑。

Imagine your idealized town made of plasticine and then deformed. I can still number the blocks and recognize the streets and avenues, though these are no longer straight and equidistant. Similarly, on our earth, longitude and latitude denote the positions of points, although there is no “ American town” construction.

0。但我仍然看到一个困难。你被迫使用你的“欧洲城镇结构”。我同意你可以对点或事件进行排序，但这种构造会混淆所有距离的测量。它不会像我的构造那样给你空间的度量特性 。举个例子。我知道，在我的美国小镇，要走十个街区，我必须走两倍于

0 . But I still see a difficulty. You are forced to use your “ European town structure” . I agree that you can order points, or events, but this construction will muddle all measurement of distances. It will not give you the metric properties of space as does my construction. Take an example. I know, in my American town, that to walk ten blocks I have to cover twice the distance of

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五个街区。因为我知道所有街区都是相等的，所以我可以立即确定距离。

five blocks. Since I know that all blocks are equal, I can immediately determine distances.

M . 确实如此。在我的“欧洲城镇”结构中，我无法通过变形块的数量立即测量距离。我必须知道更多的东西；我必须知道我的表面的几何特性。

M . That is true. In my “ European town ” structure, I cannot measure distances immediately by the number of deformed blocks. I must know something more; I must know the geometrical properties o f my surface.

正如每个人都知道赤道上 0° 到 10° 经度与北极附近 0° 到 10° 经度的距离不一样。但是每个航海家都知道如何判断地球上两个这样的点之间的距离，因为他知道地球上的几何特性。他可以根据球面三角学知识通过计算来做到这一点，也可以通过实验来做到这一点，即让船以相同的速度航行通过这两个距离。在你的例子中，整个问题很简单，因为所有街道和大道之间的距离都相同。在我们的地球的情况下，它更为复杂；0° 和 10° 两条子午线在地球的两极相交，在赤道上相距最远。同样，在我的“欧洲城镇结构”中，我必须比你的“美国城镇结构”了解更多东西，才能确定距离。

Ju st as everyone knows that from 0° to 10° longitude on the Equator is not the same distance as from 0° to 10° longitude near the North Pole. But every navigator knows how to judge the distance between two such points on our earth because he knows its geometrical properties. H e can either do it by calculations based on the knowledge of spherical trigonometry, or he can do it experimentally, sailing his ship through the two distances at the same speed. In your case the whole problem is trivial, because all the streets and avenues are the same distance apart. In the case o f our earth it is more complicated; the two meridians 0° and 10° meet at the earth’s poles and are farthest apart on the Equator. Similarly, in my ‘ ‘ European town structure” , I must know something more than you in your “ American town structure” , in order to determine distances.

我可以通过研究每个特定情况下连续体的几何特性来获得这些额外的知识。

I can gain this additional knowledge by studying the geometrical properties of my continuum in every particular case.

0。但这一切只能说明，放弃欧几里得几何的简单结构而采用你必须使用的复杂支架是多么不方便和复杂。这真的有必要吗？

0 . But all this only goes to show how inconvenient and complicated it is to give up the simple structure of the Euclidean geometry for the intricate scaffolding which you are bound to use. Is this really necessary?

恐怕是的，如果我们想应用我们的物理学

M . I am afraid it is, if we want to apply our physics

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对于任何 CS，没有神秘的惯性 CS，我同意我的数学工具比你的更复杂，但我的物理假设更简单、更自然。

to any C.S., without the mysterious inertial C.S. I agree that my mathematical tool is more complicated than yours, but my physical assumptions are simpler and more natural.

讨论仅限于二维连续体。广义相对论中争论的焦点更加复杂，因为它不是二维，而是四维时空连续体。但这些想法与二维情况下的想法相同。我们不能在广义相对论中使用平行、垂直杆和同步时钟的机械支架，就像在狭义相对论中一样。在任意 CS 中

The discussion has been restricted to two-dimensional continua. The point at issue in the general relativity theory is still more complicated, since it is not the two-dimensional, but the four-dimensional time-space continuum. But the ideas are the same as those sketched in the two-dimensional case. We cannot use in the general relativity theory the mechanical scaffolding o f parallel, perpendicular rods and synchronized clocks, as in the special relativity theory. In an arbitrary C.S.

我们不能像在狭义相对论的惯性坐标系中那样，使用刚性杆、有节奏和同步的时钟来确定事件发生的点和瞬间。我们仍然可以用非欧几里得杆和不同步的时钟来对事件进行排序。但实际测量需要刚性杆和完美的有节奏和同步的时钟，只能在局部惯性坐标系中进行。为此，整个狭义相对论都是有效的；但我们的“好”

we cannot determine the point and the instant at which an event happens by the use of rigid rods, rhythmical and synchronized clocks, as in the inertial C.S. of the special relativity theory. We can still order the events with our non-Euclidean rods and our clocks out of rhythm. But actual measurements requiring rigid rods and perfect rhythmical and synchronized clocks can be performed only in the local inertial C.S. For this the whole special relativity theory is valid; but our “ good”

CS 只是局部的，其惯性特征受限于空间和时间。即使在我们任意的 CS 中，我们也可以预见在局部惯性 CS 中进行的测量结果，但为此我们必须知道我们的时空连续体的几何特征。

C.S. is only local, its inertial character being limited in space and time. Even in our arbitrary C.S. we can foresee the results of measurements made in the local inertial C.S. But for this we must know the geometrical character of our time-space continuum.

我们理想化的实验仅仅表明了新相对论物理学的一般特征。它们告诉我们，我们的基本问题是引力问题。

O ur idealized experiments indicate only the general character of the new relativistic physics. They show us that our fundamental problem is that of gravitation.

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它们还向我们展示了广义相对论导致时间和空间概念的进一步推广。

They also show us that the general relativity theory leads to further generalization of time and space concepts.

广义相对论及其验证

G E N E R A L R E L A T I V I T Y A N D ITS V E R IF IC A T IO N

广义相对论试图为所有 CS 制定物理定律。该理论的基本问题是引力问题。自牛顿时代以来，该理论首次认真努力重新表述引力定律。这真的有必要吗？

The general theory of relativity attempts to formulate physical laws for all C.S. The fundamental problem o f the theory is that o f gravitation. The theory makes the first serious effort, since Newton’s time, to reformulate the law o f gravitation. Is this really necessary?

我们已经了解了牛顿理论的成就，了解了基于他的引力定律的天文学的巨大发展。牛顿定律仍然是所有天文计算的基础。但我们也了解了一些对旧理论的反对意见。牛顿定律只在经典物理学的惯性坐标系中有效，我们记得，在坐标系中，力学定律必须在其中有效的条件是定义的。两个物体之间的力取决于它们之间的距离。众所周知，力和距离之间的联系相对于经典变换是不变的。但这条定律不符合狭义相对论的框架。距离相对于洛伦兹变换不是不变的。我们可以尝试推广引力定律，使其符合狭义相对论，就像我们成功地推广运动定律一样，或者换句话说，将其表述为相对于洛伦兹变换而不是经典变换不变。但牛顿引力定律

We have already learned about the achievements of Newton’s theory, about the great development of astronomy based upon his gravitational law. Newton’s law still remains the basis of all astronomical calculations. But we also learned about some objections to the old theory. Newton’s law is valid only in the inertial C.S. of classical physics, in C.S. defined, we remember, by the condition that the laws of mechanics must be valid in them. The force between two masses depends upon their distance from each other. The connection between force and distance is, as we know, invariant with respect to the classical transformation. But this law does not fit the frame of special relativity. The distance is not invariant with respect to the Lorentz transformation. We could try, as we did so successfully with the laws of motion, to generalize the gravitational law, to make it fit the special relativity theory, or, in other words, to formulate it so that it would be invariant with respect to the Lorentz and not to the classical transformation. But Newton’s gravitational law op-

2 5 碳

2 5 C

固执地提出，我们尽一切努力来简化它，并把它纳入狭义相对论的框架中。即使我们成功了，还需要进一步的步骤：从狭义相对论的惯性坐标系到广义相对论的任意坐标系。另一方面，关于坠落电梯的理想化实验清楚地表明，如果不解决引力问题，就不可能制定广义相对论。

posed obstinately all our efforts to simplify and fit it into the scheme of the special relativity theory. Even if we succeeded in this, a further step would still be necessary: the step from the inertial C.S. of the special relativity theory to the arbitrary C.S. of the general relativity theory. O n the other hand, the idealized experiments about the falling lift show clearly that there is no chance o f formulating the general relativity theory without solving the problem o f gravitation.

从我们的论证中，我们看到了为什么引力问题的解决方案在古典物理学和广义相对论中会有所不同。

From our argument we see why the solution of the gravitational problem will differ in classical physics and general relativity.

我们已尽力指出通向广义相对论的道路以及迫使我们再次改变旧观点的原因。我们不必深入研究该理论的形式结构，而是描述新引力理论与旧引力理论相比的一些特点。鉴于前面所说的一切，理解这些差异的性质应该不太难。

We have tried to indicate the way leading to the general relativity theory and the reasons forcing us to change our old views once more. Without going into the formal structure of the theory, we shall characterize some features of the new gravitational theory as compared with the old. It should not be too difficult to grasp the nature of these differences in view of all that has previously been said.

（1）广义相对论的引力方程可以应用于任何坐标系。在特殊情况下选择任何特定的坐标系只是为了方便。理论上所有坐标系都是允许的。通过忽略引力，我们会自动回到狭义相对论的惯性坐标系。

(1) The gravitational equations of the general relativity theory can be applied to any C.S. It is merely a matter of convenience to choose any particular C.S. in a special case. Theoretically all C.S. are permissible. By ignoring the gravitation, we automatically come back to the inertial C.S. of the special relativity theory.

（2）牛顿引力定律把此时此刻物体的运动与远处物体同时发生的行为联系起来。这一定律构成了我们整个机械观的模式。但是

(2) Newton’s gravitational law connects the motion of a body here and now with the action of a body at the same time in the far distance. This is the law which formed a pattern for our whole mechanical view. But

机械视图损坏

the mechanical view broke 2

1down. 在麦克斯韦方程中我们认识到了自然法则的新模式。

1down. In Maxwell’s equations we realized a new pattern for the laws of nature.

麦克斯韦方程组是结构定律。它们将此时此刻发生的事件与稍后即将发生的事件联系起来。

Maxwell’s equations are structure laws. They connect events which happen now and here with events which will happen a little later in the immediate vicinity.

它们是描述电磁场变化的定律。我们新的引力方程也是描述引力场变化的结构定律。我们可以形象地说：从牛顿引力定律到广义相对论的过渡，有点类似于从包含库仑定律的电流体理论到麦克斯韦理论的过渡。

They are the laws describing the changes of the electromagnetic field. O ur new gravitational equations are also structure laws describing the changes of the gravitational field. Schematically speaking, we could say: the transition from Newton’s gravitational law to general relativity resembles somewhat the transition from the theory of electric fluids with Coulomb’s law to Maxwell’s theory.

（3）

(3)

我们的世界不是欧几里得的。我们世界的几何性质是由质量及其速度决定的。广义相对论的引力方程试图揭示我们世界的几何特性。

O ur world is not Euclidean. The geometrical nature of our world is shaped by masses and their velocities. The gravitational equations o f the general relativity theory try to disclose the geometrical properties of our world.

暂且假设我们已经成功地始终如一地执行了广义相对论的纲领。但是，我们是否面临将推测与现实相差太远的危险？我们知道旧理论对天文观测的解释有多好。是否有可能在新理论与观测之间建立一座桥梁？每一种推测都必须通过实验来检验，任何结果，无论多么有吸引力，如果与事实不符，都必须被拒绝。新的引力理论是如何经受住实验检验的？这个问题可以用一句话来回答：旧理论是一种特殊的

Let us suppose, for the moment, that we have succeeded in carrying out consistently the programme of the general relativity theory. But are we not in danger of carrying speculation too far from reality? We know how well the old theory explains astronomical observations. Is there a possibility o f constructing a bridge between the new theory and observation? Every speculation must be tested by experiment, and any results, no matter how attractive, must be rejected if they do not fit the facts. How did the new theory of gravitation stand the test of experiment? This question can be answered in one sentence: The old theory is a special

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新理论的极限情况。如果引力相对较弱，旧牛顿定律就会很好地近似于新引力定律。因此，所有支持经典理论的观察结果也支持广义相对论。我们从新理论的更高层次重新获得了旧理论。

limiting case of the new one. I f the gravitational forces are comparatively weak, the old Newtonian law turns out to be a good approximation to the new laws of gravitation. Thus all observations which support the classical theory also support the general relativity theory. We regain the old theory from the higher level of the new one.

即使没有额外的观察结果可以支持新理论，如果它的解释与旧理论一样好，那么在两种理论之间自由选择的情况下，我们不得不决定选择新理论。从形式的角度来看，新理论的方程更复杂，但从基本原理的角度来看，它们的假设要简单得多。绝对时间和惯性系统这两个可怕的幽灵已经消失。引力和惯性质量等价的线索并没有被忽视。不需要对引力及其对距离的依赖性做出任何假设。引力方程具有结构定律的形式，这是自场论取得伟大成就以来所有物理定律所要求的形式。

Even if no additional observation could be quoted in favour of the new theory, if its explanation were only just as good as the old one, given a free choice between the two theories, we should have to decide in favour of the new one. The equations o f the new theory are, from the formal point o f view, more complicated, but their assumptions are, from the point o f view o f fundamental principles, much simpler. The two frightening ghosts, absolute time and an inertial system, have disappeared. The clue of the equivalence of gravitational and inertial mass is not overlooked. No assumption about the gravitational forces and their dependence on distance is needed. The gravitational equations have the form of structure laws, the form required o f all physical laws since the great achievements of the field theory.

新的引力定律可以得出一些牛顿引力定律中没有的新推论。其中一个推论是光线在引力场中的弯曲，上面已经提到过。现在将提到另外两个推论。

Some new deductions, not contained in Newton’s gravitational law, can be drawn from the new gravitational laws. O ne, the bending o f light rays in a gravitational field, has already been quoted. Two further consequences will now be mentioned.

如果在引力较弱时旧定律遵循新定律，那么偏离

I f the old laws follow from the new one when the gravitational forces are weak, the deviations from the

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牛顿引力定律只适用于相对强大的引力。以我们的太阳系为例。行星，包括我们的地球，都沿着椭圆轨道绕太阳运行。水星是离太阳最近的行星。太阳和水星之间的吸引力比太阳和任何其他行星之间的吸引力都强，因为距离较小。如果说有希望找到牛顿定律的偏差，那么水星是最有可能的。根据经典理论，水星所描述的路径与任何其他行星的路径相同，只是它离太阳更近。根据广义相对论，运动应该略有不同。水星不仅应该绕太阳运行，而且它所描述的椭圆应该相对于与太阳相关的坐标系非常缓慢地旋转。椭圆的这种旋转表达了广义相对论的新效应。新理论

Newtonian law of gravitation can be expected only for comparatively strong gravitational forces. Take our solar system. The planets, our earth among them, move along elliptical paths around the sun. Mercury is the planet nearest the sun. The attraction between the sun and Mercury is stronger than that between the sun and any other planet, since the distance is smaller. I f there is any hope of finding a deviation from Newton’s law, the greatest chance is in the case of Mercury. It follows, from classical theory, that the path described by Mercury is of the same kind as that of any other planet except that it is nearer the sun. According to the general relativity theory, the motion should be slightly different. Not only should Mercury travel around the sun, but the ellipse which it describes should rotate very slowly, relative to the C.S. connected with the sun. This rotation of the ellipse expresses the new effect of the general relativity theory. The new theory

二十五

预测震级为 4

predicts the magnitude of 4

这种效应。水星的椭圆

this effect. Mercury’s ellipse

需要三百万年才能完成一次完整的旋转！我们看到这种影响是多么微不足道，而且在距离太阳较远的行星中寻找这种影响是多么无望。

would perform a complete rotation in three million years ! We see how small the effect is, and how hopeless it would be to seek it in the case of planets farther removed from the sun.

在广义相对论提出之前，人们就已经知道水星的运动偏离了椭圆轨道，但对此却没有给出任何解释。另一方面，广义相对论的发展并没有考虑到这个特殊问题。直到后来，人们才从新的引力方程中得出行星绕太阳运动时椭圆旋转的结论。在水星的例子中，理论成功地解释了运动偏离牛顿定律的情况。

The deviation of the motion of the planet Mercury from the ellipse was known before the general relativity theory was formulated, and no explanation could be found. O n the other hand, general relativity developed without any attention to this special problem. O nly later was the conclusion about the rotation of the ellipse in the motion of a planet around the sun drawn from the new gravitational equations. In the case of Mercury, theory explained successfully the deviation of the motion from the Newtonian law.

但是，还有另一个结论，它是从广义相对论中得出的，并与实验进行了比较。我们已经看到，放在旋转圆盘的大圆环上的时钟与放在小圆环上的时钟有不同的节奏。同样，从相对论中可以得出，放在太阳上的时钟与放在地球上的时钟有不同的节奏，因为引力场对太阳的影响比对地球的影响大得多。

But there is still another conclusion which was drawn from the general relativity theory and compared with experiment. We have already seen that a clock placed on the large circle of a rotating disc has a different rhythm from one placed on the smaller circle. Similarly, it follows from the theory o f relativity that a clock placed on the sun would have a different rhythm from one placed on the earth, since the influence of the gravitational field is much stronger on the sun than on the earth.

我们在第 103 页上指出，钠在白炽状态下会发出一定波长的均匀黄光。在这种辐射中，原子显示出其节奏之一；可以说，原子代表了时钟，而发射的波长是其节奏之一。根据

We remarked on p. 103 that sodium, when incandescent, emits homogeneous yellow light of a definite wave-length. In this radiation the atom reveals one of its rhythms; the atom represents, so to speak, a clock and the emitted wave-length one of its rhythms. Accord-

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根据广义相对论，放在太阳上的一个钠原子所发射光的波长应该比放在地球上的一个钠原子所发射光的波长稍微大一些。

ing to the general theory of relativity, the wave-length of light emitted by a sodium atom, say, placed on the sun should be very slightly greater than that of light emitted by a sodium atom on our earth.

通过观察来检验广义相对论的推论是一个复杂的问题，而且绝非完全解决。由于我们关心的是基本思想，因此我们不打算深入探讨这个问题，我们只想说，到目前为止，实验的结论似乎证实了广义相对论得出的结论。

The problem of testing the consequences o f the general relativity theory by observation is an intricate one and by no means definitely settled. As we are concerned with principal ideas, we do not intend to go deeper into this matter, and only state that the verdict of experiment seems, so far, to confirm the conclusions drawn from the general relativity theory.

领域与物质

F IE L D A N D M A T T E R

我们已经看到机械观点是如何以及为何失效的。假设简单的力作用于不变的粒子之间，是无法解释所有现象的。我们首次尝试超越机械观点并引入场概念，结果在电磁现象领域最为成功。我们制定了电磁场的结构定律；这些定律将空间和时间上彼此非常接近的事件联系起来。

We have seen how and why the mechanical point of view broke down. It was impossible to explain all phenomena by assuming that simple forces act between unalterable particles. O ur first attempts to go beyond the mechanical view and to introduce field concepts proved most successful in the domain of electromagnetic phenomena. The structure laws for the electromagnetic field were formulated; laws connecting events very near to each other in space and time.

这些定律符合狭义相对论的框架，因为它们相对于洛伦兹变换是不变的。后来，广义相对论制定了引力定律。它们也是描述物质粒子之间引力场的结构定律。麦克斯韦定律也很容易推广，以便可以应用于任何 CS，就像广义相对论的引力定律一样。

These laws fit the frame of the special relativity theory, since they are invariant with respect to the Lorentz transformation. Later the general relativity theory formulated the gravitational laws. Again they are structure laws describing the gravitational field between material particles. It was also easy to generalize M axwell’s laws so that they could be applied to any C.S., like the gravitational laws of the general relativity theory.

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我们有两种现实： 物质和场。毫无疑问，我们目前无法像十九世纪初的物理学家那样，想象整个物理学都建立在物质概念之上。目前，我们接受这两个概念。我们能把物质和场看作两种截然不同的现实吗？

We have two realities: matter and field. There is no doubt that we cannot at present imagine the whole of physics built upon the concept o f matter as the physicists of the early nineteenth century did. For the moment we accept both the concepts. C an we think of matter and field as two distinct and different realities?

给定一个小粒子，我们可以天真地想象，粒子有一个确定的表面，粒子在该表面不复存在，引力场出现。在我们的想象中，场定律有效的区域与物质存在的区域截然分开。但是，区分物质和场的物理标准是什么呢？在了解相对论之前，我们可以尝试用以下方式回答这个问题：物质有质量，而场没有质量。场代表能量，物质代表质量。但我们已经知道，鉴于所获得的进一步知识，这样的答案是不够的。从相对论中，我们知道物质代表着巨大的能量储备，能量代表着物质。我们不能以这种方式定性地区分物质和场，因为质量和能量之间的区别不是定性的。迄今为止，绝大部分能量集中在物质中；但粒子周围的场也代表能量，尽管数量要少得多。因此我们可以说：能量集中度大的地方就是物质，能量集中度小的地方就是场。但如果是这样的话，那么物质和场的区别就在于

Given a small particle o f matter, we could picture in a naive way that there is a definite surface of the particle where it ceases to exist and its gravitational field appears. In our picture, the region in which the laws o f field are valid is abruptly separated from the region in which matter is present. But what are the physical criterions distinguishing matter and field? Before we learned about the relativity theory we could have tried to answer this question in the following way: matter has mass, whereas field has not. Field represents energy, matter represents mass. But we already know that such an answer is insufficient in view of the further knowledge gained. From the relativity theory we know that matter represents vast stores of energy and that energy represents matter. We cannot, in this way, distinguish qualitatively between matter and field, since the distinction between mass and energy is not a qualitative one. By far the greatest part of energy is concentrated in matter; but the field surrounding the particle also represents energy, though in an incomparably smaller quantity. We could therefore say: Matter is where the concentration of energy is great, field where the concentration of energy is small. But if this is the case, then the difference between matter

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场是定量的而非定性的。

and field is a quantitative rather than a qualitative one.

把物质和场视为两种截然不同的性质是没有意义的。我们无法想象一个明确的表面将场和物质区分开来。

There is no sense in regarding matter and field as two qualities quite different from each other. We cannot imagine a definite surface separating distinctly field and matter.

电荷和场也存在同样的困难。似乎不可能给出一个明显的定性标准来区分物质和场或电荷和场。

The same difficulty arises for the charge and its field. It seems impossible to give an obvious qualitative criterion for distinguishing between matter and field or charge and field.

我们的结构定律，即麦克斯韦定律和引力定律，在能量极高浓度的情况下，或者说在场源（即电荷或物质）存在的情况下，就会失效。

O u r structure laws, that is, Maxwell’s laws and the gravitational laws, break down for very great concentrations of energy or, as we may say, where sources of the field, that is electric charges or matter, are present.

但是，我们能否稍微修改一下我们的方程，使它们在任何地方都有效，即使在能量高度集中的区域？

But could we not slightly modify our equations so that they would be valid everywhere, even in regions where energy is enormously concentrated?

我们不能只在物质概念的基础上建立物理学。但在承认质量和能量的等价性之后，物质和场的划分是人为的，没有明确的定义。

We cannot build physics on the basis of the matter-concept alone. But the division into matter and field is, after the recognition of the equivalence of mass and energy, something artificial and not clearly defined.

我们能否拒绝物质的概念，建立一种纯场物理学？我们感觉中物质的本质其实是能量在相对较小的空间中高度集中。我们可以将物质视为空间中场极强的区域。

Could we not reject the concept of matter and build a pure field physics? What impresses our senses as matter is really a great concentration of energy into a comparatively small space. We could regard matter as the regions in space where the field is extremely strong.

这样就可以创建一个新的哲学背景。它的最终目标是通过始终有效的结构定律来解释自然界中的所有事件。从这个角度来看，一块抛出的石头是一个变化的场，其中最大场EE的状态

In this way a new philosophical background could be created. Its final aim would be the explanation of all events in nature by structure laws valid always and everywhere. A thrown stone is, from this point of view, a changing field, where the states of greatest field E E

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强度以石头的速度在空间中传播。在我们的新物理学中，场和物质将无处容身，场是唯一的现实。

intensity travel through space with the velocity o f the stone. There would be no place, in our new physics, for both field and matter, field being the only reality.

这一新观点是由场物理学的伟大成就、我们成功地以结构定律的形式表达电、磁、引力定律以及最终的质量和能量等价性所提出的。我们的最终问题是修改我们的场定律，使它们不会在能量高度集中的区域失效。

This new view is suggested by the great achievements of field physics, by our success in expressing the laws o f electricity, magnetism, gravitation in the form of structure laws, and finally by the equivalence of mass and energy. O ur ultimate problem would be to modify our field laws in such a way that they would not break down for regions in which the energy is enormously concentrated.

但迄今为止，我们还没有成功令人信服地、始终如一地实现这一计划。至于是否有可能实现它，还得等到未来再说。目前，在我们所有的实际理论构建中，我们仍然必须假设两个现实：场和物质。

But we have not so far succeeded in fulfilling this programme convincingly and consistently. The decision, as to whether it is possible to carry it out, belongs to the future. A t present we must still assume in all our actual theoretical constructions two realities: field and matter.

我们面前仍存在一些基本问题。我们知道，所有物质都由几种粒子构成。这些基本粒子是如何构成各种物质的？这些基本粒子如何与场相互作用？通过寻找这些问题的答案，物理学中引入了新思想，即量子理论的思想。

Fundamental problems are still before us. We know that all matter is constructed from a few kinds of particles only. How are the various forms of matter built from these elementary particles? How do these elementary particles interact with the field? By the search for an answer to these questions new ideas have been introduced into physics, the ideas of the quantum theory.

我们总结一下：

W e Summarize:

物理学中出现了一个新概念，这是自牛顿时代以来最重要的 发明：场。 需要伟大的 科学想象力才能意识到它不是电荷

A new concept appears in physics, the most important invention since Newton's time: the field. It needed great scientific imagination to realize that it is not the charges

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场的 概念被证明是最 成功的，它导致了麦克斯韦方程的形成，该方程描述了电磁场的结构 并控制了电和光现象。

nor the particles but the field in the space between the charges and the particles which is essential fo r the description o f physical phenomena. The field concept proves most successful and leads to the formulation o f M axwell's equations describing the structure o f the electromagnetic field and governing the electric as well as the optical phenomena.

相对论起源于场问题。 旧理论的矛盾和不一致性迫使我们 赋予时空连续体新的属性，赋予物理世界中所有事件的发生场所新的属性。

The theory o f relativity arises from the field problems. The contradictions and inconsistencies o f the old theories force us to ascribe new properties to the time-space continuum, to the scene o f all events in our physical world.

相对论的发展分为两个阶段。第一步 是狭义相对论，它只适用于惯性坐标系，即牛顿 所制定的惯性定律有效的系统 。狭义相对论基于 两个基本假设：物理定律 在所有相对匀速运动的坐标系中都是相同的；光速始终相同 。根据这些假设， 并经过实验的充分证实，可以推导出运动杆和时钟的性质，即它们的 长度和节奏随速度的变化。

The relativity theory develops in two steps. The first step leads to what is known as the special theory o f relativity, applied only to inertial co-ordinate systems, that is, to systems in which the law o f inertia, as formulated by Newton, is valid. The special theory o f relativity is based on two fundamental assumptions: physical laws are the same in all co-ordinate systems moving uniformly, relative to each other; the velocity o f light always has the same value. From these assumptions, fu lly confirmed by experiment, the properties o f moving rods and clocks, their changes in length and rhythm depending on velocity, are deduced.

相对论改变了力学定律。 如果运动粒子的速度 接近光速，旧定律就失效了。 相对论重新表述的运动物体的新定律得到了实验的出色证实。（狭义） 相对论的另一个结果是质量和能量之间的联系 。质量就是能量，能量有质量。质量和能量这两条 守恒定律被结合在

The theory o f relativity changes the laws o f mechanics. The old laws are invalid i f the velocity o f the moving particle approaches that of light. The new laws fo r a moving body as reformulated by the relativity theory are splendidly confirmed by experiment. A further consequence o f the (special) theory o f relativity is the connection between mass and energy. Mass is energy and energy has mass. The two conservation laws o f mass and energy are combined by the

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相对论合而为一，质能守恒定律。

relativity theory into one, the conservation law o f mass-energy.

广义相对论对时空连续体进行了更深入的分析，其适用范围 不再局限于惯性坐标系。

The general theory o f relativity gives a still deeper analysis o f the time-space continuum. The validity o f the theory is no longer restricted to inertial co-ordinate systems.

该理论着手解决引力问题，制定引力场新的结构定律。

The theory attacks the problem o f gravitation and fo rmulates new structure laws fo r the gravitational field.

它迫使我们分析几何学在描述物理世界 中所起的作用。它认为引力和惯性质量相等这一事实是本质的，而 不仅仅是偶然的， 就像在经典力学中一样。广义相对论的实验结果 与经典力学的结果只有细微的差别。 只要可以进行比较，它们就能经受住实验的检验 。但该理论的力量在于其内在的 一致性和基本假设的简单性。

It forces us to analyse the role played by geometry in the description o f the physical world. It regards the fact that gravitational and inertial mass are equal, as essential and not merely accidental, as in classical mechanics. The experimental consequences o f the general relativity theory differ only slightly from those o f classical mechanics. They stand the test o f experiment well wherever comparison is possible. But the strength o f the theory lies in its inner consistency and the simplicity o f its fundamental assumptions.

相对论强调了场 概念在物理学中的重要性。但我们尚未成功制定出 纯粹的场物理学。目前我们仍然必须假设 场和物质都存在。

The theory o f relativity stresses the importance o f the field concept in physics. But we have not yet succeeded in formulating a pure field physics. For the present we must still assume the existence o f both: field and matter.

四、量子

IV. Q U A N T A

广达

Q U A N T A

连续性、 不连续性——物质和 电的基本量子——光的量子——光谱—— 物质波——概率波——物理学和现实 连续性、不连续性

Continuity, discontinuity— Elementary quanta o f matter and electricity— The quanta o f light—Light spectra— The waves o f matter—Probability waves—Physics and reality C O N T I N U I T Y , D IS C O N T I N U I T Y

纽约市及其周边地区的地图展现在我们面前。我们问：地图上的哪些地方可以乘火车到达？在火车时刻表中查找这些地点后，我们将它们标记在地图上。

A m ap of New York City and the surrounding country is spread before us. We ask: which points on this map can be reached by train? After looking up these points in a railway timetable, we mark them on the map.

现在我们换个问题：哪些点可以开车到达？如果我们在地图上画出所有从纽约出发的道路的线，这些道路上的每个点实际上都可以开车到达。

We now change our question and ask: which points can be reached by car? I f we draw lines on the map representing all the roads starting from New York, every point on these roads can, in fact, be reached by car.

在这两种情况下，我们都有一组点。在第一种情况下，它们彼此分开，代表不同的火车站，在第二种情况下，它们是沿线的点，代表道路。我们的下一个问题是这些点与纽约的距离，或者更严格地说，与该城市某个地点的距离。在第一种情况下，某些数字对应于我们地图上的点。这些数字变化不规则，但总是有限的。

In both cases we have sets of points. In the first they are separated from each other and represent the different railway stations, and in the second they are the points along the lines representing the roads. O u r next question is about the distance o f each o f these points from New York, or, to be more rigorous, from a certain spot in that city. In the first case, certain numbers correspond to the points on our map. These numbers change by irregular, but always finite, leaps and bounds.

我们说：从纽约出发，乘火车可以到达的地方的距离只以不连续的 方式变化。从纽约出发，乘火车可以到达的地方的距离只以不连续的方式变化。

We say: the distances from New York of the places which can be reached by train change only in a discontinuous way. Those of the places which can be 263

264

然而，汽车到达的距离可以按任意小的步长变化，它们可以连续变化。对于汽车，距离变化可以任意小，但对于火车则不能。

reached by car, however, may change by steps as small as we wish, they can vary in a continuous way. The changes in distance can be made arbitrarily small in the case of a car, but not in the case of a train.

煤矿的产量可以连续变化。煤炭产量可以以任意小的步长减少或增加。但矿工的就业人数只能不连续地变化。说“自昨天以来，员工人数增加了3.7 8 3 ” ，这纯粹是胡说八道。

The output of a coal mine can change in a continuous way. The amount of coal produced can be decreased or increased by arbitrarily small steps. But the number of miners employed can change only discontinuously. It would be pure nonsense to say: “ Since yesterday, the number of employees has increased by 3.7 8 3 .”

当问及口袋里有多少钱时，一个人只能给出一个只包含两位小数的数字。

Asked about the amount of money in his pocket, a man can give a number containing only two decimals.

一笔钱只能以跳跃的方式变化，不连续。在美国，最小允许变化，或者我们称之为“基本量子”

A sum of money can change only by jumps, in a discontinuous way. In America the smallest permissible change or, as we shall call it, the “ elementary quantum ”

对于美国货币，基本量子是一分钱。对于英国货币，基本量子是一法新，价值仅为美国基本量子的一半。这里有一个可以比较两个基本量子相互价值的例子。它们的价值比率具有明确的意义，因为其中一个的价值是另一个的两倍。

for American money, is one cent. The elementary quantum for English money is one farthing, worth only half the American elementary quantum. Here we have an example o f two elementary quanta whose mutual values can be compared. The ratio o f their values has a definite sense since one of them is worth twice as much as the other.

我们可以说：有些量可以连续变化，而另一些量只能不连续地变化，变化的步长不能再减小。这些不可分割的步长被称为它们所指的特定量的基本量子。

We can say: some quantities can change continuously and others can change only discontinuously, by steps which cannot be further decreased. These indivisible steps are called the elementary quanta of the particular quantity to which they refer.

我们可以称量大量的沙子，并将其质量视为连续的，尽管它的颗粒结构

We can weigh large quantities of sand and regard its mass as continuous even though its granular structure

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显而易见。但如果沙子变得非常珍贵，所用的秤非常灵敏，我们就必须考虑这样一个事实：质量总是以一粒沙子的倍数变化。这一粒沙子的质量就是我们的基本量子。从这个例子中，我们可以看到，通过提高测量精度，可以检测到一个迄今为止被认为是连续的量的不连续性。

is evident. But if the sand were to become very precious and the scales used very sensitive, we should have to consider the fact that the mass always changes by a multiple number of one grain. The mass of this one grain would be our elementary quantum. From this example we see how the discontinuous character of a quantity, so far regarded as continuous, can be detected by increasing the precision of our measurements.

如果我们必须用一句话来概括量子理论的主要思想，我们可以说：必须 假定一些迄今为止被认为 是连续的物理量是由基本量子组成的。

I f we had to characterize the principal idea of the quantum theory in one sentence, we could say: it must be assumed that some physical quantities so fa r regarded as continuous are composed o f elementary quanta.

量子理论所涉及的事实领域极其广阔，这些事实已被高度发达的现代实验技术所揭示。

The region of facts covered by the quantum theory is tremendously great. These facts have been disclosed by the highly developed technique o f modern experiment.

由于我们无法展示或描述甚至基本的实验，我们不得不经常武断地引用它们的结果。我们的目的只是解释主要的基本思想。

As we can neither show nor describe even the basic experiments, we shall frequently have to quote their results dogmatically. O ur aim is to explain the principal underlying ideas only.

基本物质量子

E L E M E N T A R Y Q U A N T A O F M A T T E R

和电力

A N D E L E C T R I C I T Y

在动能论所描绘的物质图景中，所有元素都是由分子构成的。以最简单的最轻元素氢为例。第 66 页

In the picture of matter drawn by the kinetic theory, all elements are built of molecules. Take the simplest case of the lightest element, that is hydrogen. O n p. 66

我们看到了布朗运动的研究如何导致一个氢分子质量的确定。

we saw how the study of Brownian motions led to the determination of the mass o f one hydrogen molecule.

其值为：

Its value is:

0.000 000 000 000 000 000 000 0033 克。

0.000 000 000 000 000 000 000 0033 gram.

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这意味着质量是不连续的。一部分氢的质量只能改变整数个小步骤，每个步骤对应于一个氢分子的质量。但化学过程表明氢分子可以分解成两部分，或者换句话说，氢分子由两个原子组成。在化学过程中，原子而不是分子起着基本量子的作用。将上述数字除以二，我们得到氢原子的质量。这大约是

This means that mass is discontinuous. The mass of a portion of hydrogen can change only by a whole number of small steps each corresponding to the mass of one hydrogen molecule. But chemical processes show that the hydrogen molecule can be broken up into two parts, or, in other words, that the hydrogen molecule is composed of two atoms. In chemical processes it is the atom and not the molecule which plays the role of an elementary quantum. Dividing the above number by two, we find the mass of a hydrogen atom. This is about

0.000 000 000 000 000 000 000 0017 克。

0.000 000 000 000 000 000 000 0017 gram.

质量是一个不连续的量。不过，在确定重量时，我们当然不必担心这一点。

Mass is a discontinuous quantity. But, o f course, we need not bother about this when determining weight.

即使是最灵敏的尺度也远远达不到检测质量变化不连续性的精度。

Even the most sensitive scales are far from attaining the degree o f precision by which the discontinuity in mass variation could be detected.

让我们回到一个众所周知的事实。一根导线与电流源相连。电流从高电位流过导线，流向低电位。我们记得，许多实验事实都是用电流体流过导线的简单理论来解释的。我们还记得（第 82 页），正流体从高电位流向低电位，还是负流体从低电位流向高电位，这仅仅是一个惯例问题。我们暂时不考虑场概念带来的所有进一步进展。即使以电流体的简单术语来思考，

Let us return to a well-known fact. A wire is connected with the source o f a current. The current is flowing through the wire from higher to lower potential. We remember that many experimental facts were explained by the simple theory of electric fluids flowing through the wire. We also remember (p. 82) that the decision as to whether the positive fluid flows from higher to lower potential, or the negative fluid flows from lower to higher potential, was merely a matter of convention. For the moment we disregard all the further progress resulting from the field concepts. Even when thinking in the simple terms of electric fluids,

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还有一些问题需要解决。正如“流体”这个名称所暗示的那样，早期的电被认为是连续的量。根据这些旧观点，电荷量可以以任意小的步骤改变。没有必要假设基本电量子。物质动力学理论的成就为我们准备了一个新问题：电流体的基本量子是否存在？另一个需要解决的问题是：电流是由正流体、负流体还是两种流体的流动组成的？

there still remain some questions to be settled. As the name “ fluid” suggests, electricity was regarded, in the early days, as a continuous quantity. The amount of charge could be changed, according to these old views, by arbitrarily small steps. There was no need to assume elementary electric quanta. The achievements of the kinetic theory of matter prepared us for a new question: do elementary quanta o f electric fluids exist? The other question to be settled is: does the current consist of a flow of positive, negative or perhaps of both fluids?

所有回答这些问题的实验，其目的是将电流体从导线中分离出来，让它穿过空旷的空间，使其与物质脱离，然后研究其特性，这些特性在这些条件下必定会最明显地显现出来。十九世纪末进行了许多此类实验。在解释这些实验装置的想法之前，至少在一种情况下，我们将引用结果。流过导线的电流体是负电流体，因此方向是从低电位流向高电位。如果我们从一开始就知道这一点，当电流体理论刚刚形成时，我们肯定会互换这两个词，称橡胶棒的电为正电，玻璃棒的电为负电。那么将流动的流体视为正电会更方便。由于我们的第一个猜测是错误的，我们现在不得不忍受这种不便。下一个重要问题是这种负流体的结构是否是“颗粒状的”，是否

The idea of all the experiments answering these questions is to tear the electric fluid from the wire, to let it travel through empty space, to deprive it of any association with matter and then to investigate its properties, which must appear most clearly under these conditions. M any experiments of this kind were performed in the late nineteenth century. Before explaining the idea o f these experimental arrangements, at least in one case, we shall quote the results. The electric fluid flowing through the wire is a negative one, directed, therefore, from lower to higher potential. H ad we known this from the start, when the theory of electric fluids was first formed, we should certainly have interchanged the words, and called the electricity of the rubber rod positive, that of the glass rod negative. It would then have been more convenient to regard the flowing fluid as the positive one. Since our first guess was wrong, we now have to put up with the inconvenience. The next important question is whether the structure of this negative fluid is “ granular” , whether

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它是否由电量子组成。大量独立实验再次表明，这种负电的基本量子存在是毫无疑问的。负电流体由颗粒构成，就像海滩由沙粒组成，房子由砖块砌成一样。大约四十年前，J.J.汤姆森最清楚地阐述了这一结果。负电的基本量子称为电子。因此，每个负电荷都由大量以电子为代表的基本电荷组成。负电荷只能像质量一样不连续地变化。然而，基本电荷非常小，以至于在许多研究中，将其视为连续量同样可能，有时甚至更方便。因此，原子和电子理论向科学引入了只能跳跃变化的不连续物理量。

or not it is composed of electric quanta. Again a number of independent experiments show that there is no doubt as to the existence o f an elementary quantum of this negative electricity. The negative electric fluid is constructed of grains, just as the beach is composed of grains of sand, or a house built o f bricks. This result was formulated most clearly by J . J . Thomson, about forty years ago. The elementary quanta of negative electricity are called electrons. Thus every negative electric charge is composed o f a multitude of elementary charges represented by electrons. The negative charge can, like mass, vary only discontinuously. The elementary electric charge is, however, so small that in many investigations it is equally possible and sometimes even more convenient to regard it as a continuous quantity. Thus the atomic and electron theories introduce into science discontinuous physical quantities which can vary only by jumps.

想象一下，在某个地方有两块平行的金属板，其中所有的空气都被抽走了。其中一块板带正电荷，另一块板带负电荷。带入两块板之间的正测试电荷将被带正电荷的板排斥，而被带负电荷的板吸引。因此，电场的力线将从带正电荷的板指向带负电荷的板。作用在带负电荷的测试体上的力的方向相反。

Imagine two parallel metal plates in some place from which all air has been extracted. One o f the plates has a positive, the other a negative charge. A positive test charge brought between the two plates will be repelled by the positively charged and attracted by the negatively charged plate. Thus the lines of force of the electric field will be directed from the positively to the negatively charged plate. A force acting on a negatively charged test body would have the opposite direction.

如果板足够大，它们之间的力线将在各处同样密集；测试体放在哪里、力和

I f the plates are sufficiently large, the lines o f force between them will be equally dense everywhere; it is immaterial where the test body is placed, the force and,

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因此，力线的密度将相同。

therefore, the density of the lines of force will be the same.

电子被带到极板之间的某个地方

Electrons brought somewhere between the plates

就像地球引力场中的雨滴一样，从带负电的板向带正电的板平行移动。有许多已知的实验装置可以将电子束带入这样的场中，并将它们全部引导到相同的方向。最简单的方法之一是将加热的导线放在带电板之间。这种加热的导线会发射电子，然后由外部场的力线引导电子。例如，每个人都熟悉的电子管就是基于此原理。

would behave like raindrops in the gravitational field of the earth, moving parallel to each other from the negatively to the positively charged plate. There are many known experimental arrangements for bringing a shower of electrons into such a field which directs them all in the same way. One o f the simplest is to bring a heated wire between the charged plates. Such a heated wire emits electrons which are afterwards directed by the lines o f force o f the external field. For instance, radio tubes, familiar to everyone, are based on this principle.

人们在电子束上进行了许多非常巧妙的实验。人们研究了电子在不同电场和磁场中路径的变化。人们甚至可以分离出单个电子，并确定其基本电荷和质量，即其对电子束的惯性阻力。

M any very ingenious experiments have been performed on a beam o f electrons. The changes of their path in different electric and magnetic external fields have been investigated. It has even been possible to isolate a single electron and to determine its elementary charge and its mass, that is, its inertial resistance to the

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外力作用。这里我们只引用电子的质量值。结果发现它比氢原子的质量小约两千倍 。因此，氢原子的质量虽然很小，但与电子的质量相比却显得很大。从一致场论的角度来看，电子的整个质量，即整个能量，是其场的能量；其强度的大部分在一个非常小的范围内，远离电子的“中心”，它就很弱。

action of an external force. Here we shall only quote the value of the mass of an electron. It turned out to be about two thousand times smaller than the mass o f a hydrogen atom. Thus the mass of a hydrogen atom, small as it is, appears great in comparison with the mass o f an electron. From the point of view of a consistent field theory, the whole mass, that is, the whole energy, of an electron is the energy o f its field; the bulk o f its strength is within a very small sphere, and away from the “ centre” of the electron it is weak.

我们之前说过，任何元素的原子都是其最小的基本量子。人们长期以来都相信这一说法。然而，现在人们不再相信它了！科学形成了一种新观点，表明了旧观点的局限性。在物理学中，几乎没有任何说法比关于原子复杂结构的陈述更牢固地建立在事实的基础上。首先认识到，电子，即负电流体的基本量子，也是原子的组成部分之一，是构成所有物质的基本砖块之一。前面引用的加热丝发射电子的例子只是从物质中提取这些粒子的众多实例之一。这一结果将物质结构问题与电问题紧密联系起来，毫无疑问，这是从许多独立的实验事实中得出的。

We said before that the atom o f any element is its smallest elementary quantum. This statement was believed for a very long time. Now, however, it is no longer believed ! Science has formed a new view showing the limitations of the old one. There is scarcely any statement in physics more firmly founded on facts than the one about the complex structure o f the atom. First came the realization that the electron, the elementary quantum of the negative electric fluid, is also one o f the components of the atom, one o f the elementary bricks from which all matter is built. The previously quoted example of a heated wire emitting electrons is only one o f the numerous instances o f the extraction o f these particles from matter. This result closely connecting the problem of the structure o f matter with that o f electricity, follows, beyond any doubt, from very many independent experimental facts.

从原子中提取一些组成原子的电子相对容易。这可以通过加热来实现，就像我们加热的电线的例子一样，或者

It is comparatively easy to extract from an atom some of the electrons from which it is composed. This can be done by heat, as in our example of a heated wire, or in

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以不同的方式，比如用其他电子轰击原子。

a different way, such as by bombarding atoms with other electrons.

假设将一根细的、炽热的金属线插入稀薄的氢分子中。金属线将向四面八方发射电子。在外来电场的作用下，电子将获得一定的速度。n 电子的速度增加，就像在重力场中下落的石头一样。通过这种方法，我们可以获得一束以一定的速度朝一定的方向飞奔的电子。如今，我们可以通过将电子置于非常强的场的作用下，使其速度达到与光速相当的程度。那么，当一束具有一定速度的电子撞击稀薄的氢分子时会发生什么呢？速度足够快的电子的撞击不仅会将氢分子分裂成两个原子，而且还会从其中一个原子中提取出一个电子。

Suppose a thin, red-hot, metal wire is inserted into rarefied hydrogen. The wire will emit electrons in all directions. Under the action of a foreign electric field a given velocity will be imparted to them. A n electron increases its velocity just like a stone falling in the gravitational field. By this method we can obtain a beam of electrons rushing along with a definite speed in a definite direction. Nowadays, we can reach velocities comparable to that of light by submitting electrons to the action of very strong fields. What happens, then, when a beam o f electrons o f a definite velocity impinges on the molecules o f rarefied hydrogen? The impact of a sufficiently speedy electron will not only disrupt the hydrogen molecule into its two atoms but will also extract an electron from one of the atoms.

让我们接受电子是物质的组成部分这一事实。那么，被剥离出电子的原子就不可能是电中性的。如果它以前是中性的，那么现在就不可能是中性的，因为它少了一个基本电荷。剩下的一定带正电荷。此外，由于电子的质量比最轻的原子小得多，我们可以有把握地得出结论，原子的大部分质量不是由电子表示的，而是由比电子重得多的基本粒子的剩余部分表示的。

Let us accept the fact that electrons are constituents of matter. Then, an atom from which an electron has been torn out cannot be electrically neutral. I f it was previously neutral, then it cannot be so now, since it is poorer by one elementary charge. That which remains must have a positive charge. Furthermore, since the mass of an electron is so much smaller than that o f the lightest atom, we can safely conclude that by far the greater part of the mass o f the atom is not represented by electrons but by the remainder of the elementary particles which are much heavier than the electrons.

我们将原子的这个较重部分称为 原子核。

We call this heavy part of the atom its nucleus.

现代实验物理学已经开发出方法

Modern experimental physics has developed methods

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分裂原子核，将一种元素的原子变成另一种元素的原子，以及从原子核中提取构成原子核的重基本粒子。这章物理学被称为“原子核物理学”，卢瑟福对此做出了巨大贡献，从实验的角度来看，它是最有趣的。但是，仍然缺少一种基本思想简单、能将原子核物理学领域中丰富多样的事实联系起来的理论。由于在本文中我们只对一般的物理思想感兴趣，因此我们将省略这一章，尽管它在现代物理学中非常重要。

of breaking up the nucleus of the atom, o f changing atoms of one element into those of another, and of extracting from the nucleus the heavy elementary particles of which it is built. This chapter of physics, known as “ nuclear physics” , to which Rutherford contributed so much, is, from the experimental point of view, the most interesting. But a theory, simple in its fundamental ideas and connecting the rich variety o f facts in the domain of nuclear physics, is still lacking. Since, in these pages, we are interested only in general physical ideas, we shall omit this chapter in spite o f its great importance in modern physics.

泉岛飞行表演

T H E Q U A N T A O F L IG H T

让我们设想一下建在海边的一堵墙。海浪不断冲击着墙，冲走了墙的部分表面，然后退却，为涌来的海浪让出道路。墙的质量减少了，我们可以问，比如说，一年内有多少被冲走了。但现在让我们想象一个不同的过程。我们想以不同的方式减少墙的质量，减少的量与之前相同。

Let us consider a wall built along the seashore. The waves from the sea continually impinge on the wall, wash away some o f its surface, and retreat, leaving the way clear for the incoming waves. The mass of the wall decreases and we can ask how much is washed away in, say, one year. But now let us picture a different process. We want to diminish the mass of the wall by the same amount as previously but in a different way.

我们向墙壁射击，在子弹击中的地方将墙壁击碎。墙壁的质量将减少，我们可以想象在两种情况下质量的减少是相同的。但是从墙壁的外观，我们可以很容易地检测出是连续的海浪还是不连续的子弹在起作用。在理解我们即将描述的现象时，记住这一点会很有帮助

We shoot at the wall and split it at the places where the bullets hit. The mass of the wall will be decreased and we can well imagine that the same reduction in mass is achieved in both cases. But from the appearance of the wall we could easily detect whether the continuous sea wave or the discontinuous shower of bullets has been acting. It will be helpful, in understanding the phenomena which we are about to describe, to bear in

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注意海浪和枪林弹雨之间的区别。

mind the difference between sea waves and a shower of bullets.

我们之前说过，加热的金属丝会发射电子。这里我们将介绍另一种从金属中提取电子的方法。均匀光，例如紫光，即我们所知的具有一定波长的光，照射到金属表面。光从金属中提取电子。电子从金属中分离出来，并以一定的速度喷涌而出。从能量原理的角度来看，我们可以说：光的能量部分转化为被驱逐电子的动能。现代实验技术使我们能够记录这些电子子弹，从而确定它们的速度，从而确定它们的能量。这种光照射到金属上提取电子的现象称为光电效应。

We said, previously, that a heated wire emits electrons. Here we shall introduce another way o f extracting electrons from metal. Homogeneous light, such as violet light, which is, as we know, light o f a definite wave-length, is impinging on a metal surface. The light extracts electrons from the metal. The electrons are torn from the metal and a shower o f them speeds along with a certain velocity. From the point of view o f the energy principle we can say: the energy o f light is partially transformed into the kinetic energy o f expelled electrons. Modern experimental technique enables us to register these electron-bullets, to determine their velocity and thus their energy. This extraction of electrons by light falling upon metal is called the photoelectric effect.

我们的出发点是均匀光波的作用，具有一定的强度。与每个实验一样，我们现在必须改变我们的安排，看看这是否会对观察到的效果产生影响。

O ur starting-point was the action o f a homogeneous light wave, with some definite intensity. As in every experiment, we must now change our arrangements to see whether this will have any influence on the observed effect.

让我们首先改变照射在金属板上的均匀紫光的强度，并注意发射电子的能量在多大程度上取决于光的强度。让我们尝试通过推理而不是实验来找到答案。

Let us begin by changing the intensity of the homogeneous violet light falling on the metal plate and note to what extent the energy of the emitted electrons depends upon the intensity of the light. Let us try to find the answer by reasoning instead of by experiment.

我们可以论证：在光电效应中，辐射能量的某一特定部分被转化为电子的运动能量。如果我们再次

We could argue: in the photoelectric effect a certain definite portion of the energy of radiation is transformed into energy of motion of the electrons. I f we again

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如果用相同波长但更强大的光源照射金属，那么发射电子的能量应该更大，因为辐射的能量更丰富。因此，如果光的强度增加，我们应该预期发射电子的速度也会增加。但实验再次与我们的预测相矛盾。我们再一次看到，自然法则并不像我们所希望的那样。

illuminate the metal with light of the same wave-length but from a more powerful source, then the energy o f the emitted electrons should be greater, since the radiation is richer in energy. We should, therefore, expect the velocity of the emitted electrons to increase if the intensity of the light increases. But experiment again contradicts our prediction. Once more we see that the laws of nature are not as we should like them to be.

我们遇到了一个实验，它与我们的预测相矛盾，打破了我们预测所依据的理论。从波动理论的角度来看，实际的实验结果令人震惊。

We have come upon one of the experiments which, contradicting our predictions, breaks the theory on which they were based. The actual experimental result is, from the point of view of the wave theory, astonishing.

所观察到的电子都具有相同的速度、相同的能量，当光的强度增加时，它们不会发生改变。

The observed electrons all have the same speed, the same energy, which does not change when the intensity of the light is increased.

这个实验结果是波动理论所无法预测的，这里又一个新理论在旧理论与实验的冲突中诞生了。

This experimental result could not be predicted by the wave theory. Here again a new theory arises from the conflict between the old theory and experiment.

让我们故意不公正地对待光的波动理论，忘记它的伟大成就，忘记它对光绕过非常小的障碍物时弯曲的出色解释。当我们的注意力集中在光电效应上时，让我们从理论中要求对这种效应做出充分的解释。显然，我们无法从波动理论中推断出电子的能量与从金属板中提取电子的光强度无关。

Let us be deliberately unjust to the wave theory of light, forgetting its great achievements, its splendid explanation of the bending of light around very small obstacles. With our attention focused on the photoelectric effect, let us demand from the theory an adequate explanation of this effect. Obviously, we cannot deduce from the wave theory the independence o f the energy of electrons from the intensity of light by which they have been extracted from the metal plate.

因此，我们将尝试另一种理论。我们记得，牛顿的粒子理论解释了许多观察到的光现象，但却未能解释

We shall, therefore, try another theory. We remember that Newton’s corpuscular theory, explaining many of the observed phenomena of light, failed to account

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我们现在故意忽略了光的弯曲。在牛顿时代，能量的概念并不存在。根据他的说法，光粒子没有重量；每种颜色都保留了各自的物质特性。后来，当能量的概念被创造出来，人们认识到光携带能量时，没有人想到将这些概念应用于光的粒子理论。牛顿理论已经消亡，直到我们这个世纪，它的复兴才受到重视。

for the bending o f light, which we are now deliberately disregarding. In Newton’s time the concept o f energy did not exist. Light corpuscles were, according to him, weightless; each colour preserved its own substance character. Later, when the concept o f energy was created and it was recognized that light carries energy, no one thought of applying these concepts to the corpuscular theory of light. Newton’s theory was dead and, until our own century, its revival was not taken seriously.

为了保持牛顿理论的基本思想，我们必须假设均匀光由能量颗粒组成，并用光量子（我们称之为光子）取代旧的光粒子，光量子是能量的一小部分，以光速在空旷的空间中传播。牛顿理论以这种新形式复兴，导致了 光的量子理论。 不仅物质和电荷，而且辐射能量也具有颗粒结构，即由光量子构成。

To keep the principal idea of Newton’s theory, we must assume that homogeneous light is composed o f energy-grains and replace the old light corpuscles by light quanta, which we shall call photons, small portions of energy, travelling through empty space with the velocity of light. The revival of Newton’s theory in this new form leads to the quantum theory of light. Not only matter and electric charge, but also energy of radiation has a granular structure, i.e., is built up of light quanta.

除了物质量子和电量子之外，还有能量量子。

In addition to quanta of matter and quanta of electricity there are also quanta of energy.

能量子的概念最早由普朗克在本世纪初提出，用来解释一些比光电效应复杂得多的效应。但光电效应最清楚、最简单地表明了改变我们旧观念的必要性。

The idea of energy quanta was first introduced by Planck at the beginning of this century in order to explain some effects much more complicated than the photoelectric effect. But the photo-effect shows most clearly and simply the necessity for changing our old concepts.

很明显，光的量子理论解释了光电效应。光子雨落在金属板上。辐射之间的作用

It is at once evident that this quantum theory o f light explains the photoelectric effect. A shower of photons is falling on a metal plate. The action between radiation

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物质由许多单个过程组成，在这些过程中，光子撞击原子并撕裂出电子。这些单个过程都是相似的，并且在每种情况下提取的电子都具有相同的能量。我们还知道，增加光的强度意味着，用我们的新语言来说，增加下落的光子数量。在这种情况下，不同数量的电子将从金属板中抛出，但任何一个电子的能量都不会改变。

and matter consists here of very many single processes in which a photon impinges on the atom and tears out an electron. These single processes are all alike and the extracted electron will have the same energy in every case. We also understand that increasing the intensity of the light means, in our new language, increasing the number of falling photons. In this case, a different number of electrons would be thrown out o f the metal plate, but the energy of any single one would not change.

因此我们看到该理论与观察完全一致。

Thus we see that this theory is in perfect agreement with observation.

如果一束不同颜色的均质光（比如说，红色而不是紫色）落在金属表面，会发生什么情况呢？我们不妨用实验来回答这个问题。必须测量提取的电子的能量，并将其与紫光释放的电子的能量进行比较。红光提取的电子的能量小于紫光提取的电子的能量。这意味着不同颜色的光量子的能量是不同的。红色光子的能量是紫色光子能量的一半。或者，更严格地说：属于均质颜色的光量子的能量随着波长的增加而成比例减小。能量量子和电量子之间存在本质区别。

What will happen if a beam of homogeneous light of a different colour, say, red instead of violet, falls on the metal surface? Let us leave experiment to answer this question. The energy of the extracted electrons must be measured and compared with the energy of electrons thrown out by violet light. The energy of the electron extracted by red light turns out to be smaller than the energy of the electron extracted by violet light. This means that the energy of the light quanta is different for different colours. The photons belonging to the colour red have half the energy of those belonging to the colour violet. O r, more rigorously: the energy o f a light quantum belonging to a homogeneous colour decreases proportionally as the wave-length increases. There is an essential difference between quanta o f energy and quanta o f electricity.

光的量子因波长不同而不同，而电的量子则始终相同。如果我们使用之前的类比，我们应该比较一下

Light quanta differ for every wave-length, whereas quanta of electricity are always the same. I f we were to use one of our previous analogies, we should compare

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光量子到最小的货币量子，每个国家都有所不同。

light quanta to the smallest monetary quanta, differing in each country.

让我们继续抛弃光的波动论，假设光的结构是粒状的，由光量子（即以光速在空间中传播的光子）构成。因此，在我们的新图景中，光是光子的雨滴，光子是光能的基本量子。然而，如果抛弃波动论，波长的概念就会消失。取而代之的是什么样的新概念呢？光量子的能量！用波动论术语表达的陈述可以转化为辐射量子论的陈述。例如：

Let us continue to discard the wave theory of light and assume that the structure of light is granular and is formed by light quanta, that is, photons speeding through space with the velocity of light. Thus, in our new picture, light is a shower of photons, and the photon is the elementary quantum of light energy. If, however, the wave theory is discarded, the concept of a wave-length disappears. What new concept takes its place? The energy of the light quanta! Statements expressed in the terminology of the wave theory can be translated into statements o f the quantum theory of radiation. For example:

术语

T e r m i n o l o g y o f t h e

术语

T e r m i n o l o g y o f t h e

波动理论

W a v e T h e o r y

量子理论

Q u a n t u m T h e o r y

均匀光具有

Homogeneous light has a

同质

Homogeneous

光

light

共确定的波长。

condefinite wave-length.

这

The

包含特定光子

tains photons of a definite

红端波长

wave-length of the red end

能量。能量

energy. The energy of the

频谱是两倍

of the spectrum is twice

光子的红端

photon for the red end of

紫色的一端。

that of the violet end.

光谱是

the spectrum is half that of

紫色的一端。

the violet end.

情况可以概括如下：有些现象可以用量子理论来解释，但不能用波动理论来解释。

The state o f affairs can be summarized in the following w ay: there are phenomena which can be explained by the quantum theory but not by the wave theory.

光效应就是一个例子，尽管这种现象还有其他已知现象。有些现象可以用波动理论来解释，但不能用量子理论来解释。光绕过障碍物时弯曲就是一个典型的例子。最后，还有

Photo-effect furnishes an example, though other phenomena of this kind are known. There are phenomena which can be explained by the wave theory but not by the quantum theory. The bending o f light around obstacles is a typical example. Finally, there are

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现象，例如光的直线传播，可以通过光的量子理论和波动理论同样好地解释。

phenomena, such as the rectilinear propagation of light, which can be equally well explained by the quantum and the wave theory of light.

但光究竟是什么？它是波还是光子流？我们曾经提出过类似的问题：光是波还是光粒子流？当时，我们有充分的理由抛弃光的粒子理论，接受涵盖所有现象的波动理论。然而，现在问题要复杂得多。

But what is light really? Is it a wave or a shower of photons? Once before we put a similar question when we asked: is light a wave or a shower o f light corpuscles? A t that time there was every reason for discarding the corpuscular theory of light and accepting the wave theory, which covered all phenomena. Now, however, the problem is much more complicated.

似乎不可能通过仅选择两种可能的语言中的一种来形成对光现象的一致描述。似乎我们必须有时使用一种理论，有时使用另一种理论，而有时我们可以使用其中任何一种理论。我们面临着一种新的困难。我们有两个相互矛盾的现实图景；单独来看，它们都不能完全解释光现象，但结合起来却可以！

There seems no likelihood o f forming a consistent description of the phenomena of light by a choice of only one o f the two possible languages. It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they d o !

如何将这两张图片合并在一起？

How is it possible to combine these two pictures?

我们如何理解光的这两个截然不同的方面？解释这个新困难并不容易。我们再次面临一个根本问题。

How can we understand these two utterly different aspects of light? It is not easy to account for this new difficulty. Again we are faced with a fundamental problem.

暂时让我们接受光的光子理论，并尝试借助它来理解波动理论迄今解释的事实。这样，我们将强调乍一看使这两种理论显得无法调和的困难。

For the moment let us accept the photon theory of light and try, by its help, to understand the facts so far explained by the wave theory. In this way we shall stress the difficulties which make the two theories appear, at first sight, irreconcilable.

我们记得：一束均匀的光通过

We remember: a beam of homogeneous light passing

279

通过针孔可以看到明暗相间的环（第 118 页）。

through a pinhole gives light and dark rings (p. 118).

如何抛开波动论，只用光的量子论来理解这个现象呢?光子穿过了黑洞。

How is it possible to understand this phenomenon by the help o f the quantum theory of light, disregarding the wave theory? A photon passes through the hole.

我们可以预期，如果光子穿过，屏幕会显得明亮，如果没有穿过，屏幕会显得黑暗。然而，我们发现了光环和暗环。我们可以尝试解释如下：也许黑洞边缘和光子之间存在某种相互作用，这导致了衍射环的出现。当然，这句话很难被视为一种解释。

We could expect the screen to appear light if the photon passes through and dark if it does not. Instead, we find light and dark rings. We could try to account for it as follows: perhaps there is some interaction between the rim o f the hole and the photon which is responsible for the appearance of the diffraction rings. This sentence can, of course, hardly be regarded as an explanation.

充其量，它概述了一种解释方案，至少为未来通过物质和光子之间的相互作用理解衍射提供了一些希望。

A t best, it outlines a programme for an explanation holding out at least some hope of a future understanding o f diffraction by interaction between matter and photons.

但即便是这种微弱的希望，也因我们之前讨论的另一种实验装置而破灭了。我们以两个针孔为例。均匀的光线穿过两个孔，在屏幕上形成明暗条纹。

But even this feeble hope is dashed by our previous discussion of another experimental arrangement. Let us take two pinholes. Homogeneous light passing through the two holes gives light and dark stripes on the screen.

从光量子理论的角度如何理解这一效应呢？我们可以这样说：一个光子可以穿过两个针孔中的任意一个。

How is this effect to be understood from the point of view of the quantum theory o f light? We could argue: a photon passes through either one of the two pinholes.

如果均匀光子代表基本光粒子，我们很难想象它的分裂和穿过两个孔。但效果应该与第一种情况完全一样，是亮环和暗环，而不是亮条纹和暗条纹。那么，另一个针孔的存在怎么可能完全改变效果呢？显然，光子无法穿过的孔，即使它可能

I f a photon of homogeneous light represents an elementary light particle, we can hardly imagine its division and its passage through the two holes. But then the effect should be exactly as in the first case, light and dark rings and not light and dark stripes. How is it possible then that the presence o f another pinhole completely changes the effect? Apparently the hole through which the photon does not pass, even though it may be

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在相当远的距离，光环会变成条纹！如果光子的行为像经典物理学中的粒子，它必须穿过两个孔中的一个。但在这种情况下，衍射现象似乎很难理解。

at a fair distance, changes the rings into stripes! I f the photon behaves like a corpuscle in classical physics, it must pass through one of the two holes. But in this case, the phenomena of diffraction seem quite incomprehensible.

科学迫使我们创造新的思想、新的理论。

Science forces us to create new ideas, new theories.

他们的目的是打破常常阻碍科学进步的矛盾之墙。

Their aim is to break down the wall of contradictions which frequently blocks the way of scientific progress.

科学中所有的基本思想都诞生于现实与我们试图理解的激烈冲突之中。这又是一个需要新原理来解决的问题。在我们试图解释现代物理学解释光的量子和波动方面之间的矛盾之前，我们将表明，在处理物质量子而不是光量子时会出现完全相同的困难。

A ll the essential ideas in science were born in a dramatic conflict between reality and our attempts at understanding. Here again is a problem for the solution of which new principles are needed. Before we try to account for the attempts of modern physics to explain the contradiction between the quantum and the wave aspects o f light, we shall show that exactly the same difficulty appears when dealing with quanta of matter instead o f quanta o f light.

光谱

L I G H T S P E C T R A

我们已经知道，所有物质都只由几种粒子组成。电子是第一个被发现的物质基本粒子。但电子也是负电的基本量子。

We already know that all matter is built of only a few kinds of particles. Electrons were the first elementary particles of matter to be discovered. But electrons are also the elementary quanta of negative electricity.

我们还了解到，有些现象迫使我们假设光是由基本光量子组成的，不同波长的光量子不同。在继续之前，我们必须讨论一些物理现象，其中物质和辐射起着至关重要的作用。

We learned furthermore that some phenomena force us to assume that light is composed of elementary light quanta, differing for different wave-lengths. Before proceeding we must discuss some physical phenomena in which matter as well as radiation plays an essential role.

太阳发出的辐射可以通过棱镜分解成各种成分。太阳的连续光谱

The sun emits radiation which can be split into its components by a prism. The continuous spectrum of

2 8 1

这样就可以得到太阳的光谱。可见光谱两端之间的每个波长都被表示出来。让我们再举一个例子。前面提到，钠在白炽灯下发出的是同质光，一种颜色或一种波长的光。

the sun can thus be obtained. Every wave-length between the two ends of the visible spectrum is represented. Let us take another example. It was previously mentioned that sodium when incandescent emits homogeneous light, light of one colour or one wave-length.

如果将白炽钠放在棱镜前，我们只能看到一条黄线。一般来说，如果将辐射体放在棱镜前，它发出的光就会分解成各个成分，从而显示出辐射体的光谱特征。

I f incandescent sodium is placed before the prism, we see only one yellow line. In general, if a radiating body is placed before the prism, then the light it emits is split up into its components, revealing the spectrum characteristic of the emitting body.

气体管中的电流放电会产生光源，例如用于发光广告的霓虹灯管。假设将这样的管子放在分光镜前。分光镜是一种像棱镜一样工作的仪器，但精度和灵敏度要高得多；它将光分解成各个成分，即对光进行分析。通过分光镜看到的太阳光会产生连续光谱；所有波长都显示在光谱中。但是，如果光源是电流通过的气体，光谱的特性就会有所不同。太阳光谱不是连续的多色图案，而是连续的暗背景上出现的明亮、分离的条纹。如果每条条纹非常窄，则对应一种确定的颜色，或者用波动理论的语言来说，对应一种确定的波长。例如，如果光谱中有 20 条线可见，则每条线将由 20 个数字中的一个来表示相应的波长。各种元素的蒸气具有

The discharge of electricity in a tube containing gas produces a source of light such as seen in the neon tubes used for luminous advertisements. Suppose such a tube is placed before a spectroscope. The spectroscope is an instrument which acts like a prism, but with much greater accuracy and sensitiveness; it splits light into its components, that is, it analyses it. Light from the sun, seen through a spectroscope, gives a continuous spectrum; all wave-lengths are represented in it. If, however, the source o f light is a gas through which a current o f electricity passes, the spectrum is of a different character. Instead o f the continuous, multi-coloured design of the sun’s spectrum, bright, separated stripes appear on a continuous dark background. Every stripe, if it is very narrow, corresponds to a definite colour or, in the language of the wave theory, to a definite wavelength. For example, if twenty lines are visible in the spectrum, each of them will be designated by one o f twenty numbers expressing the corresponding wavelength. The vapours of the various elements possess

282

不同的谱线系统，因此，不同的数字组合表示发射光谱的波长。没有两种元素在其特征光谱中具有相同的条纹系统，就像没有两个人拥有完全相同的指纹一样。随着物理学家们对这些谱线进行分类，定律的存在逐渐显现出来，并且有可能用一个简单的数学公式来代替一些表示各种波长度的看似不连贯的数字列。

different systems of lines, and thus different combinations of numbers designating the wave-lengths composing the emitted light spectrum. No two elements have identical systems o f stripes in their characteristic spectra, just as no two persons have exactly identical finger-prints. As a catalogue of these lines was worked out by physicists, the existence of laws gradually became evident, and it was possible to replace some o f the columns of seemingly disconnected numbers expressing the length of the various waves by one simple mathematical formula.

刚才所说的一切现在都可以翻译成光子语言了。条纹对应于某些确定的波长，或者换句话说，对应于具有确定能量的光子。因此，发光气体不会发射具有所有可能能量的光子，而只会发射具有物质特征的能量的光子。现实再次限制了可能性的丰富性。

A ll that has just been said can now be translated into the photon language. The stripes correspond to certain definite wave-lengths or, in other words, to photons with a definite energy. Luminous gases do not, therefore, emit photons with all possible energies, but only those characteristic of the substance. Reality again limits the wealth of possibilities.

特定元素（例如氢）的原子只能发射具有确定能量的光子。只有确定能量量子的发射才是允许的，其他所有量子都被禁止。为了简单起见，假设某个元素只发射一条线，即具有相当确定能量的光子。原子在发射前能量较丰富，发射后能量较贫乏。

Atoms o f a particular element, say, hydrogen, can emit only photons with definite energies. O nly the emission of definite energy quanta is permissible, all others being prohibited. Imagine, for the sake of simplicity, that some element emits only one line, that is, photons of a quite definite energy. The atom is richer in energy before the emission and poorer afterwards.

根据能量原理，必须得出这样的结论：原子的能级在发射之前较高，发射之后较低，并且两个能级之间的差值必须等于发射光子的能量。

From the energy principle it must follow that the energy level of an atom is higher before emission and lower afterwards, and that the difference between the two levels must be equal to the energy of the emitted photon.

因此，某种元素的原子只发射一种波长的辐射，也就是某种波长的光子。

Thus the fact that an atom of a certain element emits radiation of one wave-length only, that is photons of a

283

只有确定的能量，可以用不同的方式来表达：该元素的一个原子只允许有两个能级，而光子的发射对应于原子从较高能级到较低能级的跃迁。

definite energy only, could be expressed differently: only two energy levels are permissible in an atom of this element and the emission of a photon corresponds to the transition of the atom from the higher to the lower energy level.

但是，一般来说，元素光谱中会出现不止一条线。发射的光子对应于许多能量，而不是只对应于一种能量。或者，换句话说，我们必须假设原子中允许有多个能级，并且光子的发射对应于原子从较高能级到较低能级的跃迁。但至关重要的是，并非每个能级都应被允许，因为并非每个波长、并非每个光子能量都出现在元素的光谱中。与其说某些确定的线、某些确定的波长属于每个原子的光谱，不如说每个原子都有一些确定的能级，并且光量子的发射与原子从一个能级到另一个能级的跃迁有关。一般来说，能级不是连续的，而是不连续的。我们再次看到，可能性受到现实的限制。

But more than one line appears in the spectra of the elements, as a rule. The photons emitted correspond to many energies and not to one only. O r, in other words, we must assume that many energy levels are allowed in an atom and that the emission of a photon corresponds to the transition of the atom from a higher energy level to a lower one. But it is essential that not every energy level should be permitted, since not every wave-length, not every photon-energy, appears in the spectra o f an element. Instead o f saying that some definite lines, some definite wave-lengths, belong to the spectrum o f every atom, we can say that every atom has some definite energy levels, and that the emission o f light quanta is associated with the transition of the atom from one energy level to another. The energy levels are, as a rule, not continuous but discontinuous. Again we see that the possibilities are restricted by reality.

玻尔首次揭示了为什么光谱中只出现这些线，没有其他线。他的理论于 25 年前提出，描绘了一幅原子图，至少在简单情况下，元素的光谱可以通过该图计算出来，而那些看似枯燥无味、毫无关联的数字在该理论的指导下突然变得连贯起来。

It was Bohr who showed for the first time why just these and no other lines appear in the spectra. His theory, formulated twenty-five years ago, draws a picture of the atom from which, at any rate in simple cases, the spectra of the elements can be calculated and the apparently dull and unrelated numbers are suddenly made coherent in the light o f the theory.

玻尔的理论是迈向

Bohr’s theory forms an intermediate step toward a

284

更深层次、更普遍的理论，称为波或量子力学。我们的目标是在最后几页中描述该理论的主要思想。在此之前，我们必须提到另一个更特殊的理论和实验结果。

deeper and more general theory, called the wave or quantum mechanics. It is our aim in these last pages to characterize the principal ideas o f this theory. Before doing so, we must mention one more theoretical and experimental result of a more special character.

我们的可见光谱以紫色的某个波长开始，以红色的某个波长结束。换句话说，可见光谱中光子的能量始终被限制在紫色和红色光子能量形成的范围内。当然，这种限制只是人眼的特性。如果某些能级的能量差异足够大，那么就会发出紫外光 子，形成一条超出可见光谱的线。它的存在无法用肉眼检测到；必须使用照相底片。

O ur visible spectrum begins with a certain wavelength for the violet colour and ends with a certain wave-length for the red colour. O r, in other words, the energies o f the photons in the visible spectrum are always enclosed within the limits formed by the photon energies of the violet and red lights. This limitation is, of course, only a property of the human eye. I f the difference in energy of some of the energy levels is sufficiently great, then an ultraviolet photon will be sent out, giving a line beyond the visible spectrum. Its presence cannot be detected by the naked eye; a photographic plate must be used.

X 射线也由能量比可见光高得多的光子组成，换句话说，它们的波长比可见光的波长小得多，实际上小数千倍。

X-rays are also composed of photons of a much greater energy than those o f visible light, or in other words, their wave-lengths are much smaller, thousands of times smaller in fact, than those o f visible light.

但是，我们有可能通过实验确定如此小的波长吗？对于普通光来说，这已经够难的了。我们必须有小的障碍物或小孔。两个彼此非常接近的针孔，对普通光有衍射作用，而对 X 射线有衍射作用，则必须比它们小几千倍，而且彼此更接近。

But is it possible to determine such small wavelengths experimentally? It was difficult enough to do so for ordinary light. We had to have small obstacles or small apertures. Two pinholes very near to each other, showing diffraction for ordinary light, would have to be many thousands o f times smaller and closer together to show diffraction for X-rays.

那么我们如何测量这些射线的波长呢？大自然会帮助我们。

How then can we measure the wave-lengths o f these rays? Nature herself comes to our aid.

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晶体是原子的聚集体，这些原子以非常小的距离排列在完全规则的平面上。我们的图显示了晶体结构的简单模型。图中没有微小的孔径，而是由元素原子形成的极小的障碍物，这些原子以绝对规则的顺序彼此非常接近地排列。根据晶体结构理论发现，原子之间的距离非常小，以至于它们可能会对 X 射线产生衍射效应。实验证明，实际上，可以利用晶体中以规则的三维排列方式排列的这些紧密堆积的障碍物衍射 X 射线波。

A crystal is a conglomeration of atoms arranged at very short distances from each other on a perfectly regular plan. O ur drawing shows a simple model of the structure of a crystal. Instead of minute apertures, there are extremely small obstacles formed by the atoms of the element, arranged very close to each other in absolutely regular order. The distances between the atoms, as found from the theory o f the crystal structure, are so small that they might be expected to show the effect of diffraction for X-rays. Experiment proved that it is, in fact, possible to diffract the X -ra y wave by means of these closely packed obstacles disposed in the regular three-dimensional arrangement occurring in a crystal.

假设一束X射线落在一块晶体上，穿过晶体后，被记录在光子束上。

Suppose that a beam o f X-rays falls upon a crystal and, after passing through it, is recorded on a photo-

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图版。图版随后显示了衍射图。人们已经使用各种方法来研究 X 射线光谱，从衍射图推断出有关波长的数据。如果阐述所有理论和实验细节，这里用几句话就能写满几本书。在图版 III 中，我们只给出了通过各种方法之一获得的衍射图。我们再次看到了波动理论特有的暗环和亮环。在中心可以看到非衍射射线。如果晶体没有放在 X 射线和照相底片之间，则只能看到中心的光点。

graphic plate. The plate then shows the diffraction pattern. Various methods have been used to study the X -ra y spectra, to deduce data concerning the wavelength from the diffraction pattern. What has been said here in a few words would fill volumes if all theoretical and experimental details were set forth. In Plate I I I we give only one diffraction pattern obtained by one of the various methods. We again see the dark and light rings so characteristic o f the wave theory. In the centre the non-diffracted ray is visible. I f the crystal were not brought between the X-rays and the photographic plate, only the light spot in the centre would be seen.

通过这种照片，可以计算出X射线光谱的波长，另一方面，如果已知波长，就可以得出有关晶体结构的结论。

From photographs of this kind the wave-lengths of the X -ray spectra can be calculated and, on the other hand, if the wave-length is known, conclusions can be drawn about the structure of the crystal.

物质波

T H E W A V E S O F M A T T E R

如何理解元素光谱中只出现某些特征波长这一事实？

How can we understand the fact that only certain characteristic wave-lengths appear in the spectra of the elements?

在物理学中，经常发生这样的情况：通过对看似不相关的现象进行一致的类比，取得了重大进展。在这些页面中，我们经常看到在一个科学分支中创造和发展的想法后来如何成功地应用于另一个科学分支。机械和场观的发展给出了许多此类例子。已解决的问题与未解决的问题的关联可能会为我们的困难带来新的启示

It has often happened in physics that an essential advance was achieved by carrying out a consistent analogy between apparently unrelated phenomena. In these pages we have often seen how ideas created and developed in one branch o f science were afterwards successfully applied to another. The development of the mechanical and field views gives many examples o f this kind. The association of solved problems with those unsolved may throw new light on our difficulties

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PLATE III

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通过提出新的想法来发现新的东西。很容易找到表面上的类比，但实际上什么也没表达。但发现隐藏在外部差异之下的一些基本共同特征，并在此基础上形成一种新的成功理论，是一项重要的创造性工作。

by suggesting new ideas. It is easy to find a superficial analogy which really expresses nothing. But to discover some essential common features, hidden beneath a surface of external differences, to form, on this basis, a new successful theory, is important creative work.

不到十五年前，德布罗意和薛定谔开始发展所谓的波动力学，这是通过深刻而幸运的类比取得成功理论的典型例子。

The development o f the so-called wave mechanics, begun by de Broglie and Schrödinger, less than fifteen years ago, is a typical example of the achievement of a successful theory by means of a deep and fortunate analogy.

我们的出发点是一个与现代物理学无关的经典例子。我们用手握住一根很长的柔性橡胶管或一根很长的弹簧的末端，并尝试有节奏地上下移动它，使末端产生振动。然后，正如我们在许多其他例子中看到的那样，振动会以一定的速度在管子中传播，从而产生波。如果我们想象一个无限长的管子，那么一旦开始，波的各个部分就会不受干扰地进行它们的无尽旅程。

O ur starting-point is a classical example having nothing to do with modern physics. We take in our hand the end of a very long flexible rubber tube, or a very long spring, and try to move it rhythmically up and down, so that the end oscillates. Then, as we have seen in many other examples, a wave is created by the oscillation which spreads through the tube with a certain velocity. I f we imagine an infinitely long tube, then the portions of waves, once started, will pursue their endless journey without interference.

现在再举一个例子。同一根管子的两端被固定住。如果愿意的话，可以使用小提琴弦。

Now another case. The two ends of the same tube are fastened. I f preferred, a violin string may be used.

如果在橡胶管或绳索的一端产生波浪，会发生什么情况？波浪的传播过程与前面的示例相同，但很快就会被管子的另一端反射。现在我们有两个波浪：

What happens now if a wave is created at one end of the rubber tube or cord? The wave begins its journey as in the previous example, but it is soon reflected by the other end of the tube. We now have two waves:

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一个波由振动产生，另一个波由反射产生；它们沿相反方向传播并相互干扰。追踪两个波的干扰并发现由它们叠加而产生的一个波并不困难；它被称为驻波。

one creation by oscillation, the other by reflection; they travel in opposite directions and interfere with each other. It would not be difficult to trace the interference o f the two waves and discover the one wave resulting from their superposition; it is called the standing wave.

“驻波”和“波”这两个词看似互相矛盾，但它们的结合却是由两种波叠加的结果所决定的。

The two words “ standing” and “ wave” seem to contradict each other; their combination is, nevertheless, justified by the result of the superposition of the two waves.

驻波最简单的例子是两端固定的绳索的运动，即上下运动，如我们的图所示。这种运动是当两个波沿相反方向传播时，一个波压在另一个波上的结果。这种运动的特点是：只有两个端点处于静止状态。它们被称为节点。可以说，波位于两个节点之间，绳索的所有点同时达到其偏差的最大值和最小值。

The simplest example of a standing wave is the motion of a cord with the two ends fixed, an up-and-down motion, as shown in our drawing. This motion is the result of one wave lying on the other when the two are travelling in opposite directions. The characteristic feature of this motion is: only the two end-points are at rest. They are called nodes. The wave stands, so to speak, between the two nodes, all points of the cord reaching simultaneously the maxima and minima of their deviation.

但这只是最简单的驻波。

But this is only the simplest kind o f a standing wave.

还有其他的。例如，驻波可以有三个节点，两端各一个，中心还有一个。

There are others. For example, a standing wave can have three nodes, one at each end and one in the centre.

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在这种情况下，三个点始终处于静止状态。看一眼这些图就会发现，这里的波长是具有两个节点的波长的一半。同样，驻波可以有四个、五个或更多节点。每种情况下的波长都取决于节点的数量。这个数字只能是整数，并且只能通过跳跃来改变。这句话——“驻波中的节点数是 3.576”——完全是胡说八道。

In this case three points are always at rest. A glance at the drawings shows that here the wave-length is half as great as the one with two nodes. Similarly, standing waves can have four, five, and more nodes. The wavelength in each case will depend on the number of nodes. This number can only be an integer and can change only by jumps. The sentence— “ the number of nodes in a standing wave is 3.576” — is pure nonsense.

因此波长只能不连续地变化。

Thus the wave-length can only change discontinuously.

在这里，在这个最经典的问题中，我们认识到了量子理论的熟悉特征。事实上，小提琴演奏者产生的驻波更加复杂，是许多波的混合，具有两个、三个、四个、五个或更多节点，因此是几种波长的混合。物理学可以将这种混合物分析为组成它的简单驻波。或者，使用我们之前的术语，我们可以说振荡弦有其频谱，就像发射辐射的元素一样。

Here, in this most classical problem, we recognize the familiar features of the quantum theory. The standing wave produced by a violin player is, in fact, still more complicated, being a mixture of very many waves with two, three, four, five, and more nodes and, therefore, a mixture of several wave-lengths. Physics can analyse such a mixture into the simple standing waves from which it is composed. O r, using our previous terminology, we could say that the oscillating string has its spectrum, just as an element emitting radiation.

并且，与元素的光谱一样，只允许某些波长，而禁止所有其他波长。

A nd, in the same way as for the spectrum of an element, only certain wave-lengths are allowed, all others being prohibited.

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因此，我们发现振荡弦和发射辐射的原子之间存在一些相似之处。

We have thus discovered some similarity between the oscillating cord and the atom emitting radiation.

尽管这个类比看起来很奇怪，但让我们从中得出进一步的结论，并在选择它之后尝试进行比较。每种元素的原子都是由基本粒子组成的，较重的粒子构成原子核，较轻的粒子构成电子。这样的粒子系统就像一个小型声学仪器，其中产生驻波。

Strange as this analogy may seem, let us draw further conclusions from it and try to proceed with the comparison, once having chosen it. The atoms of every element are composed of elementary particles, the heavier constituting the nucleus, and the lighter the electrons. Such a system of particles behaves like a small acoustical instrument in which standing waves are produced.

然而，驻波是两个或通常是多个运动波之间干扰的结果。

Y et the standing wave is the result o f interference between two or, generally, even more moving waves.

如果我们的类比有一定道理，那么比原子更简单的排列应该对应于扩散波。最简单的排列是什么？

I f there is some truth in our analogy, a still simpler arrangement than that of the atom should correspond to a spreading wave. What is the simplest arrangement?

在我们的物质世界中，没有什么比电子更简单了，电子是一种基本粒子，不受任何力的作用，即静止或匀速运动的电子。

In our material world, nothing can be simpler than an electron, an elementary particle, on which no forces are acting, that is, an electron at rest or in uniform motion.

我们可以猜测类比链中的另一个环节：电子以原有的形式移动 -> 波

We could guess a further link in the chain of our analogy: electron moving u n if o r m ly -> waves o f a

确定的长度。这是德布罗意的新颖而勇敢的想法。

definite length. This was de Broglie’s new and courageous idea.

之前已经表明，有些现象中光表现出波状特性，而另一些现象中光表现出粒子特性。在习惯了光是波的想法之后，我们惊讶地发现，在某些情况下，例如在光电效应中，它的行为就像光子雨。现在，我们正好看到了电子的相反情况。我们习惯了

It was previously shown that there are phenomena in which light reveals its wave-like character and others in which light reveals its corpuscular character. After becoming used to the idea that light is a wave, we found, to our astonishment, that in some cases, for instance in the photoelectric effect, it behaves like a shower o f photons. Now we have just the opposite state of affairs for electrons. We accustomed ourselves

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电子是粒子，是电和物质的基本量子。研究了它们的电荷和质量。如果德布罗意的想法是正确的，那么就一定存在一些现象，在这些现象中，物质会表现出波状特性。起初，这个通过声学类比得出的结论似乎很奇怪，难以理解。运动的粒子怎么会和波有什么关系呢？但这并不是我们第一次在物理学中遇到这种困难。我们在光现象领域也遇到了同样的问题。

to the idea that electrons are particles, elementary quanta o f electricity and matter. Their charge and mass were investigated. I f there is any truth in de Broglie’s idea, then there must be some phenomena in which matter reveals its wave-like character. A t first, this conclusion, reached by following the acoustical analogy, seems strange and incomprehensible. How can a moving corpuscle have anything to do with a wave? But this is not the first time we have faced a difficulty of this kind in physics. We met the same problem in the domain of light phenomena.

基本思想在形成物理理论中起着最关键的作用。物理学书籍中充斥着复杂的数学公式。但是，思想和思想，而不是公式，是每个物理理论的开端。这些思想后来必须采用定量理论的数学形式，以便与实验进行比较。这可以通过我们现在正在处理的问题的例子来解释。主要的猜测是，均匀运动的电子在某些现象中会表现得像波。假设一个电子或一群电子，只要它们的速度都相同，就会均匀地运动。每个电子的质量、电荷和速度都是已知的。如果我们希望以某种方式将波的概念与一个或多个均匀运动的电子联系起来，我们的下一个问题必须是：波长是多少？这是一个定量问题，必须建立一个或多或少定量的理论来回答它。这确实是一件简单的事情。数学

Fundamental ideas play the most essential role in forming a physical theory. Books on physics are full of complicated mathematical formulae. But thought and ideas, not formulae, are the beginning o f every physical theory. The ideas must later take the mathematical form of a quantitative theory, to make possible the comparison with experiment. This can be explained by the example of the problem with which we are now dealing. The principal guess is that the uniformly moving electron will behave, in some phenomena, like a wave. Assume that an electron or a shower of electrons, provided they all have the same velocity, is moving uniformly. The mass, charge, and velocity of each individual electron are known. I f we wish to associate in some way a wave concept with a uniformly moving electron or electrons, our next question must be: what is the wave-length? This is a quantitative question and a more or less quantitative theory must be built up to answer it. This is indeed a simple matter. The mathe-

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德布罗意的工作在数学上非常简单，回答了这个问题，这一点令人震惊。在他的工作完成时，其他物理理论的数学技术相对而言非常微妙和复杂。处理物质波问题的数学非常简单和基本，但基本思想却深刻而深远。

matical simplicity of de Broglie’s work, providing an answer to this question, is most astonishing. A t the time his work was done, the mathematical technique o f other physical theories was very subtle and complicated, comparatively speaking. The mathematics dealing with the problem of waves o f matter is extremely simple and elementary but the fundamental ideas are deep and far-reaching.

此前，在光波和光子的情况下，已经表明，用波动语言表述的每个陈述都可以翻译成光子或光粒子的语言。电子波也是如此。对于均匀运动的电子，粒子语言是已知的。但是，用粒子语言表达的每个陈述都可以翻译成波动语言，就像光子的情况一样。两条线索规定了翻译规则。光波与电子波或光子与电子之间的类比是一条线索。我们试图对物质和光使用相同的翻译方法。狭义相对论提供了另一条线索。自然定律必须相对于洛伦兹变换不变，而不是相对于经典变换不变。

Previously, in the case of light waves and photons, it was shown that every statement formulated in the wave language can be translated into the language of photons or light corpuscles. The same is true for electronic waves. For uniformly moving electrons, the corpuscular language is already known. But every statement expressed in the corpuscular language can be translated into the wave language, just as in the case of photons. Two clues laid down the rules of translation. The analogy between light waves and electronic waves or photons and electrons is one clue. We try to use the same method of translation for matter as for light. The special relativity theory furnished the other clue. The laws of nature must be invariant with respect to the Lorentz and not to the classical transformation.

这两个线索一起决定了与移动电子相对应的波长。根据理论，以每秒 10,000 英里的速度移动的电子具有可以很容易计算的波长，并且结果发现它位于与 X 射线波长相同的区域。因此，我们进一步得出结论，如果物质的波动性

These two clues together determine the wave-length corresponding to a moving electron. It follows from the theory that an electron moving with a velocity of, say, 10,000 miles per second, has a wave-length which can be easily calculated, and which turns out to lie in the same region as the X -ray wave-lengths. Thus we conclude further that if the wave character of matter

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可以被检测到，应该以类似于 X 射线的方式进行实验。

can be detected, it should be done experimentally in an analogous way to that o f X-rays.

想象一束以给定速度均匀移动的电子束，或者用波的术语来说，是均匀的电子波，并假设它落在非常薄的晶体上，起到衍射光栅的作用。晶体中衍射障碍物之间的距离非常小，以至于可以产生X射线的衍射。人们可能期望波长相同级的电子波也会出现类似的效果。照相底片会记录电子波穿过薄层晶体时的衍射。事实上，实验产生了无疑是该理论的伟大成就之一：电子波的衍射现象。从图 III 中的图案比较可以看出，电子波的衍射和 X 射线的衍射之间的相似性特别明显。我们知道，这样的图片使我们能够确定 X 射线的波长。这同样适用于电子波。衍射图给出了物质波的长度，理论和实验之间完美的定量一致性完美地证实了我们的论证链。

Imagine an electron beam moving uniformly with a given velocity, or, to use the wave terminology, a homogeneous electronic wave, and assume that it falls on a very thin crystal, playing the part o f a diffraction grating. The distances between the diffracting obstacles in the crystal are so small that diffraction for X-rays can be produced. One might expect a similar effect for electronic waves with the same order of wave-length. A photographic plate would register this diffraction o f electronic waves passing through the thin layer o f crystal. Indeed, the experiment produces what is undoubtedly one of the great achievements of the theory: the phenomenon of diffraction for electronic waves. The similarity between the diffraction of an electronic wave and that of an X -ray is particularly marked as seen from a comparison of the patterns in Plate I I I . We know that such pictures enable us to determine the wave-lengths of X-rays. The same holds good for electronic waves. The diffraction pattern gives the length of a wave of matter and the perfect quantitative agreement between theory and experiment confirms the chain o f our argument splendidly.

这一结果拓宽并加深了我们先前遇到的困难。这可以通过一个类似于光波的例子来说明。射向一个非常小的孔的电子会像光波一样弯曲。照相底片上会出现亮环和暗环。也许有希望解释

O u r previous difficulties are broadened and deepened by this result. This can be made clear by an example similar to the one given for a light wave. A n electron shot at a very small hole will bend like a light wave. Light and dark rings appear on the photographic plate. There may be some hope of explaining

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这种现象是由于电子和边缘之间的相互作用引起的，尽管这种解释似乎不太有希望。但是两个针孔呢？出现的是条纹而不是环。另一个孔的存在怎么可能完全改变效果呢？电子是不可分割的，似乎只能穿过两个孔中的一个。

this phenomenon by the interaction between the electron and the rim, though such an explanation does not seem to be very promising. But what about the two pinholes? Stripes appear instead of rings. How is it possible that the presence of the other hole completely changes the effect? The electron is indivisible and can, it would seem, pass through only one o f the two holes.

穿过空穴的电子怎么可能知道在远处有另一个空穴存在呢？

How could an electron passing through a hole possibly know that another hole has been made some distance away?

我们以前问过：光是什么？它是粒子雨还是波？我们现在问：什么是物质？什么是电子？它是粒子还是波？电子在外部电场或磁场中运动时表现得像粒子。当被晶体衍射时，它表现得像波。在物质的基本量子中，我们遇到了与光量子相同的困难。科学的最新进展提出的最基本问题之一是如何调和物质和波的两种矛盾观点。这是那些基本困难之一，一旦形成，从长远来看，必然会导致科学进步。物理学试图解决这个问题。

We asked before: what is light? Is it a shower o f corpuscles or a wave? We now ask: what is matter, what is an electron? Is it a particle or a wave? The electron behaves like a particle when moving in an external electric or magnetic field. It behaves like a wave when diffracted by a crystal. With the elementary quanta of matter we came across the same difficulty that we met with in the light quanta. One of the most fundamental questions raised by recent advance in science is how to reconcile the two contradictory views of matter and wave. It is one of those fundamental difficulties which, once formulated, must lead, in the long run, to scientific progress. Physics has tried to solve this problem.

未来必须决定现代物理学提出的解决方案是持久的还是暂时的。

The future must decide whether the solution suggested by modern physics is enduring or temporary.

概率波

P R O B A B I L I T Y W A V E S

根据经典力学，如果我们知道给定质点的位置和速度，以及作用的外力，那么我们可以预测

If, according to classical mechanics, we know the position and velocity o f a given material point and also what external forces are acting, we can predict, from

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力学定律，即其整个未来路径。“质点在某时刻具有某位置和速度”这句话在经典力学中具有明确的含义。如果这句话失去意义，我们关于预测未来路径的论证（第 32 页）就会失败。

the mechanical laws, the whole o f its future path. The sentence: “ The material point has such-and-such position and velocity at such-and-such an instant,” has a definite meaning in classical mechanics. I f this statement were to lose its sense, our argument (p. 32) about foretelling the future path would fail.

十九世纪初，科学家想把所有物理学归结为作用于物质粒子的简单力，这些粒子在任意时刻都有确定的位置和速度。让我们回想一下，在开始探索物理问题领域时，我们在讨论力学时是如何描述运动的。我们沿着一条确定的路径画出点，表示物体在特定时刻的准确位置，然后画出切向量，表示速度的方向和大小。这既简单又令人信服。

In the early nineteenth century, scientists wanted to reduce all physics to simple forces acting on material particles that have definite positions and velocities at any instant. Let us recall how we described motion when discussing mechanics at the beginning of our journey through the realm o f physical problems. We drew points along a definite path showing the exact positions of the body at certain instants and then tangent vectors showing the direction and magnitude of the velocities. This was both simple and convincing.

但对于我们物质的基本量子，即电子，或能量量子，即光子，我们无法重复这一过程。我们无法以在经典力学中想象运动的方式来描绘光子或电子的旅程。两个针孔的例子清楚地说明了这一点。电子和光子似乎穿过了这两个孔。因此，不可能通过以旧的经典方式描绘电子或光子的路径来解释这种效应。

But it cannot be repeated for our elementary quanta of matter, that is electrons, or for quanta o f energy, that is photons. We cannot picture the journey o f a photon or electron in the way we imagined motion in classical mechanics. The example of the two pinholes shows this clearly. Electron and photon seem to pass through the two holes. It is thus impossible to explain the effect by picturing the path of an electron or a photon in the old classical way.

当然，我们必须假设存在基本作用，例如电子或光子穿过空穴。物质和能量的基本量子的存在是毋庸置疑的。但基本定律当然不能用

We must, o f course, assume the presence o f elementary actions, such as the passing o f electrons or photons through the holes. The existence of elementary quanta of matter and energy cannot be doubted. But the elementary laws certainly cannot be formulated by

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以经典力学的简单方式指定任意时刻的位置和速度。

specifying positions and velocities at any instant in the simple manner of classical mechanics.

因此，让我们尝试一些不同的东西。让我们不断重复相同的基本过程。电子一个接一个地被发送到针孔的方向。这里使用“电子”这个词是为了明确起见；我们的论证也适用于光子。

Let us, therefore, try something different. Let us continually repeat the same elementary processes. One after the other, the electrons are sent in the direction of the pinholes. The word “ electron” is used here for the sake of definiteness; our argument is also valid for photons.

同样的实验以完全相同的方式重复了一遍又一遍；所有的电子都具有相同的速度并沿着两个针孔的方向移动。

The same experiment is repeated over and over again in exactly the same way; the electrons all have the same velocity and move in the direction of the two pinholes.

毋庸置疑，这是一个理想化的实验，在现实中无法实现，但完全可以想象。我们无法在特定时刻发射单个光子或电子，就像从枪中发射子弹一样。

It need hardly be mentioned that this is an idealized experiment which cannot be carried out in reality but may well be imagined. We cannot shoot out single photons or electrons at given instants, like bullets from a gun.

重复实验的结果必定是一个孔中出现暗色和亮色的环，两个孔中出现暗色和亮色的条纹。但有一个本质区别。对于单个电子，实验结果是难以理解的。当实验重复多次时，结果就更容易理解了。我们现在可以说：许多电子落在哪里，就会出现亮色条纹。在较少电子落在哪里，条纹会变暗。完全黑暗的斑点意味着没有电子。当然，我们不能假设所有电子都穿过其中一个孔。如果是这样，另一个孔是否被覆盖也不会有丝毫区别。但我们已经知道，覆盖另一个孔

The outcome of repeated experiments must again be dark and light rings for one hole and dark and light stripes for two. But there is one essential difference. In the case o f one individual electron, the experimental result was incomprehensible. It is more easily understood when the experiment is repeated many times. We can now say: light stripes appear where many electrons fall. The stripes become darker at the place where fewer electrons are falling. A completely dark spot means that there are no electrons. We are not, of course, allowed to assume that all the electrons pass through one o f the holes. I f this were so, it could not make the slightest difference whether or not the other is covered. But we already know that covering the

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第二个孔确实有所不同。由于一个粒子是不可分割的，我们无法想象它会穿过两个孔。实验重复多次的事实指出了另一种出路。一些电子可能穿过第一个孔，另一些电子穿过第二个孔。我们不知道为什么单个电子会选择特定的孔，但重复实验的最终结果一定是两个针孔都参与了将电子从源传输到屏幕的过程。如果我们只说明重复实验时电子群会发生什么，而不关心单个粒子的行为，那么环状和条纹图像之间的差异就变得可以理解了。通过讨论一系列实验，一个新的想法诞生了，即一群个体的行为不可预测。我们无法预测单个电子的走向，但我们可以预测，最终结果将是屏幕上出现明暗条纹。

second hole does make a difference. Since one particle is indivisible, we cannot imagine that it passes through both the holes. The fact that the experiment was repeated many times points to another way out. Some of the electrons may pass through the first hole and others through the second. We do not know why individual electrons choose particular holes, but the net result of repeated experiments must be that both pinholes participate in transmitting the electrons from the source to the screen. I f we state only what happens to the crowd of electrons when the experiment is repeated, not bothering about the behaviour o f individual particles, the difference between the ringed and the striped pictures becomes comprehensible. By the discussion of a sequence of experiments a new idea was born, that of a crowd with the individuals behaving in an unpredictable way. We cannot foretell the course o f one single electron, but we can predict that, in the net result, the light and dark stripes will appear on the screen.

我们暂时不要讨论量子物理学。

Let us leave quantum physics for the moment.

我们在经典物理学中看到，如果我们知道某一时刻物质点的位置和速度以及作用于该物质点的力，我们就可以预测其未来的路径。我们还看到了机械观点如何应用于物质的动力学理论。但在这个理论中，一个新的想法从我们的推理中产生了。彻底掌握这个想法将有助于理解后面的论证。

We have seen in classical physics that if we know the position and velocity o f a material point at a certain instant and the forces acting upon it, we can predict its future path. We also saw how the mechanical point of view was applied to the kinetic theory o f matter. But in this theory a new idea arose from our reasoning. It will be helpful in understanding later arguments to grasp this idea thoroughly.

有一个装有气体的容器。在尝试

There is a vessel containing gas. In attempting to

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要追踪每个粒子的运动，首先必须找到初始状态，即所有粒子的初始位置和速度。即使这是可能的，由于必须考虑的粒子数量巨大，将结果记录在纸上也需要超过一个人的一生的时间。如果试图采用经典力学的已知方法来计算粒子的最终位置，困难将是无法克服的。原则上，可以使用用于行星运动的方法，但在实践中这是无用的，必须让位于统计方法。这种方法不需要任何关于初始状态的精确知识。我们对系统在任何特定时刻的了解较少，因此无法说出它的过去或未来。我们对单个气体粒子的命运变得漠不关心。我们的问题性质不同。例如：我们不问，

trace the motion o f every particle one would have to commence by finding the initial states, that is, the initial positions and velocities o f all the particles. Even if this were possible, it would take more than a human lifetime to set down the result on paper, owing to the enormous number of particles which would have to be considered. I f one then tried to employ the known methods of classical mechanics for calculating the final positions o f the particles, the difficulties would be insurmountable. In principle, it is possible to use the method applied for the motion o f planets, but in practice this is useless and must give way to the method o f statistics. This method dispenses with any exact knowledge o f initial states. We know less about the system at any given moment and are thus less able to say anything about its past or future. We become indifferent to the fate of the individual gas particles. O ur problem is of a different nature. For example: we do not ask,

“此刻每个粒子的速度是多少？”

“ What is the speed of every particle at this m om ent?”

但是我们可能会问：“有多少粒子的速度在每秒 1000 到 1100 英尺之间？”我们并不关心个体。我们试图确定的是代表整个集合的平均值。很明显，只有当系统由大量个体组成时，统计推理方法才有意义。

But we may ask: “ How many particles have a speed between 1000 and 1100 feet per second?” We care nothing for individuals. What we seek to determine are average values typifying the whole aggregation. It is clear that there can be some point in a statistical method of reasoning only when the system consists o f a large number of individuals.

通过应用统计方法，我们无法预测群体中个体的行为。我们只能预测个体以某种特定方式行事的机会或概率。如果我们的统计方法

By applying the statistical method we cannot foretell the behaviour of an individual in a crowd. We can only foretell the chance, the probability, that it will behave in some particular manner. I f our statistical

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定律告诉我们，三分之一的粒子的速度在每秒 1000 到 1100 英尺之间，这意味着通过对许多粒子进行重复观察，我们确实会获得这个平均值，或者换句话说，在这个极限内找到粒子的概率等于三分之一。

laws tell us that one-third of the particles have a speed between 1000 and 1100 feet per second, it means that by repeating our observations for many particles, we shall really obtain this average, or in other words, that the probability o f finding a particle within this limit is equal to one-third.

同样，了解一个大社区的出生率并不意味着了解某个家庭是否有幸生下孩子，而是意味着了解统计结果，其中个人因素并不起任何作用。

Similarly, to know the birth rate o f a great community does not mean knowing whether any particular family is blessed with a child. It means a knowledge of statistical results in which the contributing personalities play no role.

通过观察大量汽车的车牌，我们很快就能发现其中三分之一的数字可以被三整除。但我们无法预测下一刻驶过的汽车是否具有这一特性。统计定律只能应用于大型集合，而不能应用于其个体成员。

By observing the registration plates of a great many cars we can soon discover that one-third of their numbers are divisible by three. But we cannot foretell whether the car which will pass in the next moment will have this property. Statistical laws can be applied only to big aggregations, but not to their individual members.

现在我们可以回到我们的量子问题了。

We can now return to our quantum problem.

量子物理定律具有统计特性。这意味着：它们不涉及单个系统，而是涉及相同系统的集合；它们不能通过单个系统的测量来验证，而只能通过一系列重复测量来验证。

The laws o f quantum physics are o f a statistical character. This means: they concern not one single system but an aggregation of identical systems; they cannot be verified by measurement of one individual, but only by a series o f repeated measurements.

放射性衰变是量子物理学试图为众多事件制定规则来控制从一种元素到另一种元素的自发嬗变。例如，我们知道，在 1600 年

Radioactive disintegration is one of the many events for which quantum physics tries to formulate laws governing the spontaneous transmutation from one element to another. We know, for example, that in 1600

年内，一克镭的一半会衰变，另一半会留下来。我们可以大致预测

years half o f one gram of radium will disintegrate, and half will remain. We can foretell approximately how

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许多原子将在接下来的半小时内解体，但即使在理论描述中，我们也无法说明为什么只有这些特定的原子会解体。

many atoms will disintegrate during the next half-hour, but we cannot say, even in our theoretical descriptions, why just these particular atoms are doomed.

根据我们目前的知识，我们无法指定注定要解体的单个原子。原子的命运并不取决于它的年龄。没有丝毫规律可以控制它们的个体行为。只能制定统计规律，即控制大量原子的规律。

According to our present knowledge, we have no power to designate the individual atoms condemned to disintegration. The fate o f an atom does not depend on its age. There is not the slightest trace o f a law governing their individual behaviour. O n ly statistical laws can be formulated, laws governing large aggregations of atoms.

再举一个例子。将某种元素的发光气体放在分光镜前，显示出确定波长的谱线。出现一组不连续的确定波长是原子现象的特征，在这些现象中，基本量子的存在得以揭示。但这个问题还有另一个方面。有些光谱线非常清晰，有些则较暗。清晰的谱线意味着发射出相对大量的属于该特定波长的光子；暗的谱线意味着发射出相对少量的属于该波长的光子。理论再次只给我们统计性质的陈述。

Take another example. The luminous gas of some element placed before a spectroscope shows lines of definite wave-length. The appearance of a discontinuous set of definite wave-lengths is characteristic o f the atomic phenomena in which the existence o f elementary quanta is revealed. But there is still another aspect of this problem. Some of the spectrum lines are very distinct, others are fainter. A distinct line means that a comparatively large number o f photons belonging to this particular wave-length are emitted; a faint line means that a comparatively small number of photons belonging to this wave-length are emitted. Theory again gives us statements of a statistical nature only.

每条线都对应着从高能级到低能级的跃迁。理论只告诉我们这些可能跃迁的概率，但没有告诉我们单个原子的实际跃迁。该理论之所以有效，是因为所有这些现象都涉及大集合，而不是单个个体。

Every line corresponds to a transition from higher to lower energy level. Theory tells us only about the probability of each of these possible transitions, but nothing about the actual transition of an individual atom. The theory works splendidly because all these phenomena involve large aggregations and not single individuals.

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看起来，新量子物理学与物质运动论有些相似，因为两者都具有统计性质，并且都涉及大集合。但事实并非如此！在这个类比中，不仅要了解相似之处，还要了解差异，这一点至关重要。物质运动论和量子物理学之间的相似性主要在于它们的统计特性。但差异是什么呢？

It seems that the new quantum physics resembles somewhat the kinetic theory o f matter, since both are of a statistical nature and both refer to great aggregations. But this is not so ! In this analogy an understanding not only of the similarities but also of the differences is most important. The similarity between the kinetic theory of matter and quantum physics lies chiefly in their statistical character. But what are the differences?

如果我们想知道一个城市里有多少 20 岁以上的男性和女性，我们必须让每个公民填写“男性”标题下的表格，

I f we wish to know how many men and women over the age of twenty live in a city, we must get every citizen to fill up a form under the headings “ m ale” ,

“女性”和“年龄”。只要每个答案都正确，我们就可以通过计数和分类获得统计结果。表格上的个人姓名和地址无关紧要。我们的统计观点是通过对个案的了解获得的。同样，在物质的动力学理论中，我们有控制聚合的统计定律，这些定律是在个体定律的基础上获得的。

“ female” , and “ age” . Provided every answer is correct, we can obtain, by counting and segregating them, a result of a statistical nature. The individual names and addresses on the forms are of no account. O ur statistical view is gained by the knowledge of individual cases. Similarly, in the kinetic theory of matter, we have statistical laws governing the aggregation, gained on the basis o f individual laws.

但在量子物理学中，情况完全不同。在这里，统计定律是直接给出的。个别定律被抛弃了。在光子或电子和两个针孔的例子中，我们已经看到，我们无法像在经典物理学中那样描述基本粒子在空间和时间中的可能运动。量子物理学抛弃了基本粒子的个别定律，直接陈述了支配聚集的统计定律。根据量子物理学，不可能描述基本粒子的位置和速度，也不可能预测其运动。

But in quantum physics the state of affairs is entirely different. Here the statistical laws are given immediately. The individual laws are discarded. In the example of a photon or an electron and two pinholes we have seen that we cannot describe the possible motion of elementary particles in space and time as we did in classical physics. Quantum physics abandons individual laws of elementary particles and states directly the statistical laws governing aggregations. It is impossible, on the basis of quantum physics, to describe positions and velocities of an elementary particle or to predict its

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未来的道路与经典物理学一样。量子物理学只处理聚合体，其定律适用于群体，而不适用于个人。

future path as in classical physics. Quantum physics deals only with aggregations, and its laws are for crowds and not for individuals.

迫使我们改变旧有经典观点的，是迫切的需要，而不是推测或对新奇事物的渴望。应用旧观点的困难只在一个例子中被概述过，那就是衍射现象。但可以列举许多其他同样令人信服的例子。我们试图理解现实，不断迫使我们改变观点。

It is hard necessity and not speculation or a desire for novelty which forces us to change the old classical view. The difficulties o f applying the old view have been outlined for one instance only, that o f diffraction phenomena. But many others, equally convincing, could be quoted. Changes of view are continually forced upon us by our attempts to understand reality.

但我们是否选择了唯一可能的出路，以及是否可以找到更好的方法解决我们的困难，都只能留待未来来决定。

But it always remains for the future to decide whether we chose the only possible way out and whether or not a better solution of our difficulties could have been found.

我们不得不放弃将个别情况描述为空间和时间中的客观事件；我们必须引入统计性质的定律。这些是现代量子物理学的主要特征。

We have had to forsake the description o f individual cases as objective happenings in space and time; we have had to introduce laws of a statistical nature. These are the chief characteristics o f modern quantum physics.

以前，在介绍新的物理现实（例如电磁场和引力场）时，我们试图用一般术语来指出方程的特征，通过这些方程，我们可以用数学公式来表达这些思想。现在，我们将对量子物理学做同样的事情，只简要地参考一下波尔、德布罗意、薛定谔、海森堡、狄拉克和玻恩的工作。

Previously, when introducing new physical realities, such as the electromagnetic and gravitational field, we tried to indicate in general terms the characteristic features of the equations through which the ideas have been mathematically formulated. We shall now do the same with quantum physics, referring only very briefly to the work o f Bohr, de Broglie, Schrödinger, Heisenberg, Dirac and Born.

让我们考虑一个电子的情况。这个电子可能受到任意外部电磁场的影响，也可能不受任何外部影响。

Let us consider the case of one electron. The electron may be under the influence of an arbitrary foreign electromagnetic field, or free from all external influences.

例如，它可能在原子场中移动

It may move, for instance, in the field of an atomic

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原子核或晶体上发生衍射。量子物理学教我们如何为这些问题制定数学方程。

nucleus or it may diffract on a crystal. Quantum physics teaches us how to formulate the mathematical equations for any of these problems.

我们已经认识到，一方面，振荡弦、鼓膜、管乐器或任何其他声学乐器与另一方面，辐射原子之间存在相似性。控制声学问题的数学方程和控制量子物理问题的数学方程之间也存在一些相似性。但是，在这两种情况下确定的量的物理解释也完全不同。描述振荡弦和辐射原子的物理量具有完全不同的含义，尽管方程在形式上有些相似。在弦的情况下，我们询问任意点在任意时刻偏离其正常位置的情况。知道了振荡弦在某一时刻的形状，我们就知道了我们想要的一切。因此，可以根据振荡弦的数学方程计算出任何其他时刻的偏离正常位置的情况。弦的每个点都与某个确定的偏离正常位置的情况相对应，这一事实可以更严格地表达如下：对于任何时刻，偏离正常值的情况都是弦坐标的函数。弦上的所有点都形成一个一维连续体，偏差是在这个一维连续体中定义的函数，可以通过振荡弦的方程计算出来。

We have already recognized the similarity between an oscillating cord, the membrane of a drum, a wind instrument, or any other acoustical instrument on the one hand, and a radiating atom on the other. There is also some similarity between the mathematical equations governing the acoustical problem and those governing the problem of quantum physics. But again the physical interpretation of the quantities determined in these two cases is quite different. The physical quantities describing the oscillating cord and the radiating atom have quite a different meaning, despite some formal likeness in the equations. In the case o f the cord, we ask about the deviation of an arbitrary point from its normal position at an arbitrary moment. Knowing the form of the oscillating cord at a given instant, we know everything we wish. The deviation from the normal can thus be calculated for any other moment from the mathematical equations for the oscillating cord. The fact that some definite deviation from the normal position corresponds to every point o f the cord is expressed more rigorously as follows: for any instant, the deviation from the normal value is a function of the co-ordinates o f the cord. A ll points o f the cord form a one-dimensional continuum, and the deviation is a function defined in this one-dimensional continuum, to be calculated from the equations of the oscillating cord.

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类似地，对于电子，对于空间中的任意一点和任意时刻，都会确定一个特定的函数。我们将此函数称为概率波。在我们的类比中，概率波对应于声学问题中偏离正常位置的情况。概率波在给定时刻是三维连续体的函数，而对于弦，偏差在给定时刻是一维连续体的函数。概率波构成了我们对所考虑的量子系统的知识目录，并使我们能够回答有关该系统的所有合理的统计问题。它不会告诉我们电子在任何时刻的位置和速度，因为这样的问题在量子物理学中毫无意义。但它会告诉我们在特定位置遇到电子的概率，或者我们最有可能遇到电子的地方。结果不是指一次测量，而是指多次重复测量。

Analogously, in the case o f an electron a certain function is determined for any point in space and for any moment. We shall call this function the probability wave. In our analogy the probability wave corresponds to the deviation from the normal position in the acoustical problem. The probability wave is, at a given instant, a function o f a three-dimensional continuum, whereas, in the case o f the cord the deviation was, at a given moment, a function of the one-dimensional continuum. The probability wave forms the catalogue of our knowledge of the quantum system under consideration and will enable us to answer all sensible statistical questions concerning this system. It does not tell us the position and velocity of the electron at any moment because such a question has no sense in quantum physics. But it will tell us the probability o f meeting the electron on a particular spot, or where we have the greatest chance o f meeting an electron. The result does not refer to one, but to many repeated measurements.

因此，量子物理方程决定概率波，就像麦克斯韦方程决定电磁场，引力方程决定引力场一样。量子物理定律又是结构定律。但这些量子物理方程所确定的物理概念的意义比电磁场和引力场要抽象得多；它们只是提供了回答统计问题的数学方法。

Thus the equations o f quantum physics determine the probability wave just as Maxwell’s equations determine the electromagnetic field and the gravitational equations determine the gravitational field. The laws o f quantum physics are again structure laws. But the meaning o f physical concepts determined by these equations o f quantum physics is much more abstract than in the case o f electromagnetic and gravitational fields; they provide only the mathematical means o f answering questions o f a statistical nature.

到目前为止，我们已经考虑了一些电子

So far we have considered the electron in some ex-

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外部场。如果它不是电子，即最小的电荷，而是包含数十亿个电子的可观电荷，我们就可以无视整个量子理论，按照我们旧的前量子物理学来处理这个问题。说到导线中的电流、带电导体、电磁波，我们可以应用麦克斯韦方程中包含的旧简单物理学。但是，在谈到光电效应、谱线强度、放射性、电波衍射以及许多其他揭示物质和能量量子特性的现象时，我们不能这样做。那么，可以说，我们必须再上一层楼。在经典物理学中，我们谈论的是单个粒子的位置和速度，而现在我们必须考虑概率波，在与这个单粒子问题相对应的三维连续体中。

ternal field. I f it were not the electron, the smallest possible charge, but some respectable charge containing billions of electrons, we could disregard the whole quantum theory and treat the problem according to our old pre-quantum physics. Speaking o f currents in a wire, o f charged conductors, o f electromagnetic waves, we can apply our old simple physics contained in Maxwell’s equations. But we cannot do this when speaking o f the photoelectric effect, intensity o f spectral lines, radioactivity, diffraction o f electric waves and many other phenomena in which the quantum character of matter and energy is revealed. We must then, so to speak, go one floor higher. Whereas in classical physics we spoke of positions and velocities of one particle, we must now consider probability waves, in a three-dimensional continuum corresponding to this one-particle problem.

如果我们以前学过如何从经典物理学的角度来处理类似的问题，那么量子物理学就会给出自己处理问题的方法。

Quantum physics gives its own prescription for treating a problem if we have previously been taught how to treat an analogous problem from the point of view of classical physics.

对于一个基本粒子，电子或光子，我们在三维连续体中得到概率波，如果实验经常重复，则概率波可以描述系统的统计行为。但是，如果相互作用的粒子不止一个，而是两个，例如两个电子、电子和光子，或者电子和原子核，那该怎么办呢？我们不能单独处理它们，也不能通过三维概率波来描述它们，因为它们相互之间有相互作用。

For one elementary particle, electron or photon, we have probability waves in a three-dimensional continuum, characterizing the statistical behaviour of the system if the experiments are often repeated. But what about the case of not one but two interacting particles, for instance, two electrons, electron and photon, or electron and nucleus? We cannot treat them separately and describe each of them through a probability wave in three dimensions, just because of their mutual inter-

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作用。事实上，猜测如何在量子物理学中描述由两个相互作用的粒子组成的系统并不困难。我们必须下降一层，暂时回到经典物理学。空间中两个物质点的位置在任何时刻都由六个数字表示，每个点三个。

action. Indeed, it is not very difficult to guess how to describe in quantum physics a system composed of two interacting particles. We have to descend one floor, to return for a moment to classical physics. The position o f two material points in space, at any moment, is characterized by six numbers, three for each of the points.

两个物质点的所有可能位置形成一个六维连续体，而不是像单点那样形成三维连续体。如果我们现在再上升一层，进入量子物理学，我们将在六维连续体中得到概率波，而不是像单粒子那样在三维连续体中得到概率波。同样，对于三、四或更多粒子，概率波将是九维、十二维或更多维连续体中的函数。

A ll possible positions of the two material points form a six-dimensional continuum and not a three-dimensional one as in the case of one point. I f we now again ascend one floor, to quantum physics, we shall have probability waves in a six-dimensional continuum and not in a three-dimensional continuum as in the case of one particle. Similarly, for three, four, and more particles the probability waves will be functions in a continuum of nine, twelve, and more dimensions.

这清楚地表明，概率波比存在于我们的三维空间中并传播的电磁场和引力场更为抽象。多维连续体构成了概率波的背景，只有对于一个粒子，维数才等于物理空间的维数。概率波的唯一物理意义是，它使我们能够回答多粒子和单粒子情况下合理的统计问题。因此，例如，对于一个电子，我们可以问在某个特定位置遇到电子的概率。对于两个粒子，我们的问题可能是：在给定时刻，两个粒子在两个确定位置相遇的概率是多少？

This shows clearly that the probability waves are more abstract than the electromagnetic and gravitational field existing and spreading in our three-dimensional space. The continuum of many dimensions forms the background for the probability waves, and only for one particle does the number of dimensions equal that of physical space. The only physical significance of the probability wave is that it enables us to answer sensible statistical questions in the case of many particles as well as of one. Thus, for instance, for one electron we could ask about the probability of meeting an electron in some particular spot. For two particles our question could b e : what is the probability of meeting the two particles at two definite spots at a given instant?

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我们脱离经典物理学的第一步是放弃将个案描述为空间和时间中的客观事件。我们被迫应用概率波提供的统计方法。

O u r first step away from classical physics was abandoning the description of individual cases as objective events in space and time. We were forced to apply the statistical method provided by the probability waves.

一旦选择了这条路，我们就必须进一步走向抽象，必须引入对应于多粒子问题的多维概率波。

O nce having chosen this way, we are obliged to go further toward abstraction. Probability waves in many dimensions corresponding to the many-particle problem must be introduced.

为了简洁起见，我们把量子物理以外的所有物理都称为经典物理。经典物理和量子物理有着根本的区别。经典物理旨在描述空间中存在的物体，并制定支配它们随时间变化的规律。

Let us, for the sake of briefness, call everything except quantum physics, classical physics. Classical and quantum physics differ radically. Classical physics aims at a description of objects existing in space, and the formulation o f laws governing their changes in time.

但是，揭示物质和辐射的粒子性和波动性的现象，以及放射性衰变、衍射、谱线发射等基本事件的明显统计特征，以及许多其他事件，迫使我们放弃了这种观点。量子物理学的目的不是描述空间中的单个物体及其随时间的变化。量子物理学中没有这样的陈述：“这个物体是某某，具有某种属性。”而是这样的陈述：“有某种概率，单个物体是某某，具有某种属性。”量子物理学中没有支配单个物体随时间变化的定律。相反，我们有支配概率随时间变化的定律。

But the phenomena revealing the particle and wave nature o f matter and radiation, the apparently statistical character o f elementary events such as radioactive disintegration, diffraction, emission o f spectral lines, and many others, forced us to give up this view. Quantum physics does not aim at the description of individual objects in space and their changes in time. There is no place in quantum physics for statements such as: “ This object is so-and-so, has this-and-this property.” Instead we have statements of this kind: “ There is such-and-such a probability that the individual object is so-and-so and has this-and-this property.” There is no place in quantum physics for laws governing the changes in time o f the individual object. Instead, we have laws governing the changes in time of the probability.

只有量子理论给物理学带来的这一根本性变化，才使得充分

O nly this fundamental change, brought into physics by the quantum theory, made possible an adequate

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解释物质和辐射基本量子揭示其存在的现象领域中事件的明显不连续和统计特征。

explanation of the apparently discontinuous and statistical character o f events in the realm o f phenomena in which the elementary quanta of matter and radiation reveal their existence.

然而，新的、更困难的问题出现了，这些问题至今尚未得到明确解决。我们只提及其中一些尚未解决的问题。科学不是、也永远不会是一本封闭的书。每一个重要的进步都会带来新的问题。从长远来看，每一个发展都会揭示新的、更深的困难。

Yet new, still more difficult problems arise which have not been definitely settled as yet. We shall mention only some o f these unsolved problems. Science is not and will never be a closed book. Every important advance brings new questions. Every development reveals, in the long run, new and deeper difficulties.

我们已经知道，在一个或多个粒子的简单情况下，我们可以从经典描述上升到量子描述，从空间和时间事件的客观描述上升到概率波。但我们还记得经典物理学中最重要的场概念。我们如何描述物质的基本量子和场之间的相互作用？如果十个粒子的量子描述需要三十维的概率波，那么场的量子描述就需要无限维的概率波。从经典场概念过渡到量子物理学中概率波的相应问题是一个非常困难的一步。在这里上升一层并非易事，迄今为止为解决这个问题所做的所有尝试都必须被视为不令人满意。还有另一个基本问题。在我们关于从经典物理学过渡到量子物理学的所有论证中，我们都使用了旧的前相对论描述，其中空间和时间被不同地处理。然而，如果我们

We already know that in the simple case of one or many particles we can rise from the classical to the quantum description, from the objective description of events in space and time to probability waves. But we remember the all-important field concept in classical physics. How can we describe interaction between elementary quanta of matter and field? I f a probability wave in thirty dimensions is needed for the quantum description of ten particles, then a probability wave with an infinite number of dimensions would be needed for the quantum description o f a field. The transition from the classical field concept to the corresponding problem of probability waves in quantum physics is a very difficult step. Ascending one floor is here no easy task and all attempts so far made to solve the problem must be regarded as unsatisfactory. There is also one other fundamental problem. In all our arguments about the transition from classical physics to quantum physics we used the old pre-relativistic description in which space and time are treated differently. If, however, we

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如果我们尝试从相对论提出的经典描述开始，那么我们解决量子问题就会变得更加复杂。这是现代物理学要解决的另一个问题，但还远未得到完整和令人满意的解决。对于构成原子核的重粒子，形成一致的物理学仍然存在进一步的困难。尽管有许多实验数据和许多试图阐明核问题的尝试，但我们仍然对这个领域的一些最基本的问题一无所知。

try to begin from the classical description as proposed by the relativity theory, then our ascent to the quantum problem seems much more complicated. This is another problem tackled by modern physics, but still far from a complete and satisfactory solution. There is still a further difficulty in forming a consistent physics for heavy particles, constituting the nuclei. In spite of the many experimental data and the many attempts to throw light on the nuclear problem, we are still in the dark about some of the most fundamental questions in this domain.

毫无疑问，量子物理学解释了非常丰富的事实，并且在很大程度上实现了理论与观察之间的完美一致。

There is no doubt that quantum physics explained a very rich variety of facts, achieving, for the most part, splendid agreement between theory and observation.

新量子物理学使我们与旧的机械观点相去甚远，而且退回到以前的立场似乎比以往任何时候都更加不可能。但毫无疑问，量子物理学仍然必须以物质和场这两个概念为基础。从这个意义上讲，它是一种二元论理论，并没有使我们将一切归结为场概念的旧问题更接近实现。

The new quantum physics removes us still further from the old mechanical view, and a retreat to the former position seems, more than ever, unlikely. But there is also no doubt that quantum physics must still be based on the two concepts: matter and field. It is, in this sense, a dualistic theory and does not bring our old problem of reducing everything to the field concept even one step nearer realization.

进一步的发展是否会沿着量子物理学选择的路线进行，或者更有可能将新的革命性思想引入物理学？

Will the further development be along the line chosen in quantum physics, or is it more likely that new revolutionary ideas will be introduced into physics?

前进的道路是否会像过去一样再次出现急转弯？

Will the road o f advance again make a sharp turn, as it has so often done in the past?

在过去的几年里，量子物理学的所有困难都集中在几个主要问题上。物理学正在等待它们的解决，这对

During the last few years all the difficulties of quantum physics have been concentrated around a few principal points. Physics awaits their solution impa-

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但没有办法预见这些困难何时何地能够得到澄清。

tiently. But there is no way o f foreseeing when and where the clarification of these difficulties will be brought about.

物理与现实

P H Y S IC S A N D R E A L I T Y

从这里所概括的仅代表最基本思想的物理学发展中可以得出哪些一般结论？

What are the general conclusions which can be drawn from the development o f physics indicated here in a broad outline representing only the most fundamental ideas?

科学不仅仅是定律的集合，一份不相关事实的目录。它是人类思想的创造，具有自由发明的思想和概念。物理理论试图形成现实的图景，并将其与广阔的感官印象世界建立联系。因此，我们心理结构的唯一理由是我们的理论是否以及如何形成这样的联系。

Science is not just a collection o f laws, a catalogue o f unrelated facts. It is a creation of the human mind, with its freely invented ideas and concepts. Physical theories try to form a picture of reality and to establish its connection with the wide world o f sense im pressions. Thus the only justification for our mental structures is whether and in what way our theories form such a link.

我们已经看到了物理学进步所创造的新现实。但这一创造链可以追溯到物理学的起点之外。最原始的概念之一就是物体。

We have seen new realities created by the advance of physics. But this chain of creation can be traced back far beyond the starting point of physics. One of the most primitive concepts is that of an object.

一棵树、一匹马以及任何物质物体的概念都是在经验的基础上获得的创造，尽管与物理现象世界相比，它们产生的印象是原始的。

The concepts of a tree, a horse, any material body, are creations gained on the basis of experience, though the impressions from which they arise are primitive in comparison with the world of physical phenomena.

猫逗弄老鼠时，也会通过思维创造出自己的原始现实。猫对遇到的任何老鼠都会做出类似反应，这一事实表明，它形成了概念和理论，这些概念和理论是它在自己的感觉印象世界中的指南。

A cat teasing a mouse also creates, by thought, its own primitive reality. The fact that the cat reacts in a similar way toward any mouse it meets shows that it forms concepts and theories which are its guide through its own world of sense impressions.

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“三棵树”不同于“两棵树”。“两棵树”也不同于“两块石头”。2、3、4……这些纯数字的概念脱离了它们产生的对象，是思维的创造，描述了我们世界的现实。

“ Three trees” is something different from “ two trees” . Again “ two trees” is different from “ two stones” . The concepts of the pure numbers 2, 3, 4, . . . , freed from the objects from which they arose, are creations of the thinking mind which describe the reality of our world.

心理上对时间的主观感觉使我们能够整理印象，说明一个事件先于另一个事件。但是，通过使用时钟将每个瞬间与数字联系起来，将时间视为一维连续体，这已经是一种发明。

The psychological subjective feeling o f time enables us to order our impressions, to state that one event precedes another. But to connect every instant o f time with a number, by the use of a clock, to regard time as a one-dimensional continuum, is already an invention.

欧几里得几何和非欧几里得几何的概念也是如此，我们的空间被理解为三维连续体。

So also are the concepts of Euclidean and non-Euclidean geometry, and our space understood as a three-dimensional continuum.

物理学实际上是从质量、力和惯性系统的发明开始的。这些概念都是自由发明。它们导致了机械观点的形成。对于十九世纪初的物理学家来说，我们外部世界的现实是由粒子组成的，粒子之间有简单的力作用，而且只取决于距离。他试图尽可能长时间地保持他的信念，相信他能用这些基本的现实概念成功地解释自然界的所有事件。与磁针偏转有关的困难、与以太结构有关的困难，促使我们创造了一种更微妙的现实。电磁场这一重要发明出现了。需要有勇敢的科学想象力才能充分认识到，不是物体的行为，而是

Physics really began with the invention o f mass, force, and an inertial system. These concepts are all free inventions. They led to the formulation o f the mechanical point o f view. For the physicist o f the early nineteenth century, the reality o f our outer world consisted o f particles with simple forces acting between them and depending only on the distance. H e tried to retain as long as possible his belief that he would succeed in explaining all events in nature by these fundamental concepts o f reality. The difficulties connected with the deflection o f the magnetic needle, the difficulties connected with the structure o f the ether, induced us to create a more subtle reality. The important invention of the electromagnetic field appears. A courageous scientific imagination was needed to realize fully that not the behaviour o f bodies, but

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它们之间某种东西的行为，也就是场，对于排序和理解事件可能至关重要。

the behaviour of something between them, that is, the field, may be essential for ordering and understanding events.

后来的发展既摧毁了旧的概念，又创造了新的概念。相对论抛弃了绝对时间和惯性坐标系。所有事件的背景不再是一维时间和三维空间连续体，而是四维时空连续体，这是另一个自由发明，具有新的变换特性。惯性坐标系不再需要。每个坐标系都同样适合描述自然界中的事件。

Later developments both destroyed old concepts and created new ones. Absolute time and the inertial co-ordinate system were abandoned by the relativity theory. The background for all events was no longer the one-dimensional time and the three-dimensional space continuum, but the four-dimensional time-space continuum, another free invention, with new transformation properties. The inertial co-ordinate system was no longer needed. Every co-ordinate system is equally suited for the description of events in nature.

量子理论再次为我们的现实创造了新的、本质的特征。不连续性取代了连续性。概率定律取代了支配个人的定律。

The quantum theory again created new and essential features of our reality. Discontinuity replaced continuity. Instead of laws governing individuals, probability laws appeared.

现代物理学所创造的现实确实与早期的现实相去甚远。但每一种物理理论的目的仍然是一样的。

The reality created by modem physics is, indeed, far removed from the reality of the early days. But the aim of every physical theory still remains the same.

借助物理理论，我们试图在观察到的事实迷宫中找到出路，理清和理解我们感官印象的世界。我们希望观察到的事实能够从我们的现实概念中逻辑地得出。如果不相信我们能够用我们的理论构建来把握现实，如果不相信我们世界的内在和谐，就不可能有科学。这种信念是并且将永远是所有科学创造的基本动机。在我们所有的努力中，在每一个戏剧性的

W ith the help of physical theories we try to find our way through the maze of observed facts, to order and understand the world o f our sense impressions. We want the observed facts to follow logically from our concept of reality. Without the belief that it is possible to grasp the reality with our theoretical constructions, without the belief in the inner harmony of our world, there could be no science. This belief is and always will remain the fundamental motive for all scientific creation. Throughout all our efforts, in every dramatic

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通过新旧观点之间的斗争，我们认识到，人们对于理解有着永恒的渴望，对世界和谐有着坚定的信念，而理解的障碍越来越多，这种信念也不断得到加强。

struggle between old and new views, we recognize eternal longing for understanding, the ever-firm belief in the harmony of our world, continually strengthened by the increasing obstacles to comprehension.

我们总结一下：

W e Su m m a r ize:

原子领域中各种事实的增加

A g a i n th e r ic h v a r ie ty o f f a c t s in th e r e a lm o f a t o m ic

这些现象迫使我们提出新的物理概念。

p h e n o m e n a f o r c e s u s to in v e n t n e w p h y s i c a l c o n c e p ts .

事情

M a t t e r

哈萨颗粒结构；它由精神粒子组成，

h a s a g r a n u la r s t r u c t u r e ; i t i s c o m p o s e d o f e le m e n ta r y p a r t i c l e s ,

这就是物质的本质。因此， 电荷有

th e e le m e n ta r y q u a n ta o f m a tte r . T h u s , the e le c tr ic c h a r g e h a s

无颗粒结构和——最重要的是从

a g r a n u la r s tr u c tu re a n d — m o s t im p o r t a n t f r o m th e p o i n t o f

看看等量论——哈能量也是如此。

v ie w o f th e q u a n tu m th e o ry — so h a s e n e rg y .

光子

P h o t o n s a re the

组成光的能量量子。

energy q u a n ta o f w h i c h l i g h t is c o m p o s e d .

我有轻微的光子波动吗？

I s l i g h t a w a v e o r a s h o w e r o f p h o t o n s ?

我照耀

I s a b e a m o f

电子技术是否具有磁波粒子？这些

e le c tr o n s a s h o w e r o f e le m e n ta r y p a r t i c l e s o r a w a v e ? T h e s e

通过实验来强化物理学的基本问题。

f u n d a m e n t a l q u e s tio n s a re f o r c e d u p o n p h y s ic s b y e x p e r im e n t .

为了回答这些问题，我们必须放弃描述

I n s e e k in g to a n s w e r th e m w e h a v e to a b a n d o n th e d e s c r ip tio n

空间和时间中发生的原子事件， 我们必须

o f a t o m ic e v e n ts a s h a p p e n in g s in s p a c e a n d t im e , w e h a v e to

远离旧有的机械观点。

re tre a t s t i l l f u r t h e r f r o m th e o l d m e c h a n ic a l v i e w .

量子

Q u a n t u m

物理规律统治着群体而非个人。

p h y s ic s f o r m u l a t e s l a w s g o v e r n in g c r o w d s a n d n o t in d i v i d u a l s .

不是属性而是概率被描述， 不是法律被制定，而是法律统治着系统的未来

N o t p r o p e r tie s b u t p r o b a b il it i e s a re d e s c r ib e d , n o t l a w s d is c lo s in g th e f u t u r e o f s y s te m s a re f o r m u l a t e d , b u t l a w s g o v e r n in g

概率和相关因素随时间的变化

th e c h a n g e s in tim e o f th e p r o b a b il it i e s a n d r e la t in g to g r e a t

个人聚会。

c o n g r e g a tio n s o f in d i v i d u a l s .

指数

I N D E X

指数

i n d e x

绝对运动，180，224

Absolute motion, 180, 224

衍射

Diffraction

亚里士多德，6

Aristotle, 6

（续）

( co ntinu ed)

光，119

of light, 119

X 射线，286

of X-rays, 286

黑色, 39, 40, 51

Black, 39, 40, 51

偶极子：

Dipole:

波尔，283，302

Bohr, 283, 302

电动，84

electric, 84

出生，302

Born, 302

磁性，85

magnetic, 85

布朗，63，64

Brown, 63, 64

狄拉克，302

Dirac, 302

布朗运动，63-67

Brownian movement, 63-67

色散，102，117

Dispersion, 102, 117

运动的动态画面，216

Dynamic picture of motion, 216

热量，43

Caloric, 43

速度变化，10，18，23-

Change in velocity, 10, 18, 23-

电的：

Electric:

24, 28

收费，80-82

charge, 80-82

经典变换，171

Classical transformation, 171

目前，88

current, 88

指挥，74

Conductors, 74

潜力，80-82

potential, 80-82

运动常数，49

Constant of the motion, 49

物质，74

substances, 74

连续体：

Continuum:

电磁：

Electromagnetic:

一维，210

one-dimensional, 210

领域，151

field, 151

二维，211

two-dimensional, 211

光理论，157

theory of light, 157

三维，212

three-dimensional, 212

波浪，154

wave, 154

四维，219

four-dimensional, 219

电子波，292

Electronic wave, 292

点的坐标，168

Co-ordinate of a point, 168

电子，268

Electrons, 268

坐标系，162，163

Co-ordinate system, 162, 163

验电器，71

Electroscope, 71

哥白尼，161，223，224

Copernicus, 161, 223, 224

初级：

Elementary:

光粒子，99，100，275

Corpuscles of light, 99, 100, 275

磁偶极子，85

magnetic dipoles, 85

库仑，79，86

Coulomb, 79, 86

粒子，206

particles, 206

关键实验，44-45

Crucial experiments, 44-45

量子，264

quantum, 264

水晶，285

Crystal, 285

电池的元素，88

Elements of a battery, 88

CS，163

C.S., 163

活力：

Energy:

目前，88

Current, 88

动能, 49, 50

kinetic, 49, 50

诱导，88

induced, 88

级别，282

level, 282

机械，51

mechanical, 51

德布罗意，287，290，302

de Broglie, 287, 290, 302

潜力, 49, 50

potential, 49, 50

德谟克利特，56

Democritus, 56

乙醚，112，115，120，123-126，

Ether, 112, 115, 120, 123-126,

衍射：

Diffraction:

172, 175, 1 7 6 , 1 79, 1 8 0 -

电子波，293

of electronic wave, 293

184

318

法拉第，129，142

Faraday, 129, 142

万有引力定律，30

Law of gravitation, 30

场，131

Field, 131

惯性，8，160

of inertia, 8, 160

代表权，131

representation, 131

运动，31

of motion, 31

静态，141

static, 141

莱布尼茨，25岁

Leibnitz, 25

结构，149，152

structure of, 149, 152

光在引力作用下弯曲

Light, bending in gravitational

菲索，96岁

Fizeau, 96

字段，234，252

field, 234, 252

参考框架，163

Frame of reference, 163

同质的，103

homogeneous, 103

菲涅尔，118

Fresnel, 118

量子，275

quanta, 275

力量, 11, 19, 24, 28

Force, 11, 19, 24, 28

物质，102-104

substance, 102-104

行，130

lines, 130

白色，101

white, 101

问题，56

matter, 56

洛伦兹变换，198-

Lorentz transformation, 198-

202

伽利略相对论原理，165

Galilean relativity principle, 165

伽利略，5,7,8,9,39,56,94,

Galileo, 5, 7, 8, 9, 39, 56, 94,

马斯，34

Mass, 34

95，96

95, 96

能源，208

energy, 208

加尔瓦尼，88岁

Galvani, 88

一个电子，270

of one electron, 270

概括，20

Generalization, 20

一个氢原子，266

of one hydrogen atom, 266

广义相对论，36，224

General relativity, 36, 224

一个氢分子，

of one hydrogen molecule,

引力质量，36，227，230

Gravitational mass, 36, 227, 230

67，265

67, 265

物质=能量，54

Matter = energy, 54

热火，38，41，42

Heat, 38, 41, 42

字段，256

field, 256

容量，41

capacity, 41

马克斯韦尔，129

Maxwell, 129

能源，50-55

energy, 50-55

麦克斯韦方程组，148，149，

Maxwell’s equations, 148, 149,

具体, 41

specific, 41

150, 153

物质，42，43

substance, 42, 43

梅耶尔，51岁

Mayer, 51

海森堡，302

Heisenberg, 302

热机械当量，

Mechanical equivalent of heat,

亥姆霍兹，58，59

Helmholtz, 58, 59

赫兹，129，156

Hertz, 129, 156

机械视图，59，87，92，

Mechanical view, 59, 87, 92,

惠更斯，110，111

Huygens, 110, 111

120, 124, 157

水星，253

Mercury, 253

感应电流，142

Induced current, 142

度量属性, 246

Metric properties, 246

惯性质量，36，227，230

Inertial mass, 36, 227, 230

迈克尔逊，97，183

Michelson, 97, 183

系统, 166, 220, 221

system, 166, 220, 221

分子，59

Molecules, 59

系统, 本地, 228, 229

system, local, 228, 229

数量，66

number of, 66

绝缘子，71，74

Insulators, 71, 74

莫利，183

Morley, 183

不变，170

Invariant, 170

牛顿，5, 8, 9, 25, 79, 92, 100,

Newton, 5, 8, 9, 25, 79, 92, 100,

焦耳，51，52，53

Joule, 51, 52, 53

101

节点，288

Nodes, 288

动力学理论，59-67

Kinetic theory, 59-67

核物理学，272

Nuclear physics, 272

细胞核，271

Nucleus, 271

光谱，可见光，102，284

Spectrum, visible, 102, 284

静态的运动图像，216

Static picture of motion, 216

奥斯特，90，91

Oersted, 90, 91

统计数据，298

Statistics, 298

同步时钟，190，191

Synchronized clocks, 190, 191

光电效应， 273

Photoelectric effect, 273

光子，275

Photons, 275

温度，38-40

Temperature, 38-40

紫外线，284

ultraviolet, 284

测试主体，130

Test body, 130

普朗克，275

Planck, 275

磁极，83

Pole, magnetic, 83

汤姆森，J.J.，268

Thomson, J . J ., 268

碧玺晶体，121

Tourmaline crystal, 121

原理,11

P rin cip ia , 11

概率，298

Probability, 298

变换定律，169

Transformation laws, 169

波浪，304

wave, 304

两门新科学, 10, 94

T w o N e w Sciences, 10, 94

托勒密，223，224

Ptolemy, 223, 224

匀速运动，9

Uniform motion, 9

放射性衰变，299

Radioactive disintegration, 299

物质，206

matter, 206

向量，12-19

Vectors, 12-19

镭，206

Radium, 206

电磁速度

Velocity of electromagnetic

汇率，52

Rate of exchange, 52

波浪，155

wave, 155

直线运动，12

Rectilinear motion, 12

光，97

of light, 97

光的传播，97，99，

propagation of light, 97, 99,

矢量，21

vector, 21

120

沃尔特，88，89

Volta, 88, 89

光的反射，99

Reflection of light, 99

伏打电池，88

Voltaic battery, 88

折射，98，99，115，116

Refraction, 98, 99, 115, 116

相对匀速运动，180

Relative uniform motion, 180

波浪，104

Wave, 104

相对论，186

Relativity, 186

长度，106，117

length, 106, 117

一般，36，224

general, 36, 224

纵向, 108, 121

longitudinal, 108, 121

特别, 224

special, 224

飞机，110

plane, 110

静质量，205

Rest mass, 205

球形，109

spherical, 109

罗默，96岁

Roemer, 96

站立，288

standing, 288

罗兰，92岁

Rowland, 92

光理论，110

theory of light, 110

拉姆福德，45，47，51

Rumford, 45, 47, 51

横向, 108, 121

transverse, 108, 121

卢瑟福，272

Rutherford, 272

速度，106

velocity, 106

失重

Weightless

物质，

substances,

43岁，

43,

薛定谔，287，302

Schrödinger, 287, 302

钠，103

Sodium, 103

螺线管，136

Solenoid, 136

X射线，284-286

X-rays, 284-286

狭义相对论，224

Special relativity, 224

光谱线，280

Spectral lines, 280

杨，118岁

Young, 118

剑桥：印刷者

CAMBRIDGE : PRINTED BY

W. LEW IS，文学硕士

W . LEW IS, M .A.

在大学出版社

AT THE UNIVERSITY PRESS

文档大纲

Document Outline

封面
Front cover
前言
Preface
致谢
Acknowledgments
内容
Contents
车牌列表
- 布朗运动
- 光的衍射
- 光谱线、X 射线和电子波的衍射
List of plates
- Brownian movement
- Diffraction of light
- Spectral lines, diffraction of X-rays and of electronic waves
一、机械观的兴起
- 伟大的神秘故事
- 第一个线索
- 向量
- 运动之谜
- 一条线索依然存在
- 热是物质吗？
- 逆转
- 汇率
- 哲学背景
- 物质动能论
I. The rise of the mechanical view
- The great mystery story
- The first clue
- Vectors
- The riddle of motion
- One clue remains
- Is heat a substance?
- The switchback
- The rate of exchange
- The philosophical background
- The kinetic theory of matter
二、机械观的衰落
- 两种电流体
- 磁性流体
- 第一个严重的困难
- 光速
- 光作为物质
- 颜色之谜
- 什么是波？
- 光的波动说
- 纵向光波还是横向光波？
- 以太与机械观
II. The decline of the mechanical view
- The two electric fluids
- The magnetic fluids
- The first serious difficulty
- The velocity of light
- Light as substance
- The riddle of colour
- What is a wave?
- The wave theory of light
- Longitudinal or transverse light waves?
- Ether and the mechanical view
三、场、相对论
- 场作为表征
- 场论的两大支柱
- 该领域的现实
- 场与以太
- 机械脚手架
- 以太与运动
- 时间、距离、相对论
- 相对论和力学
- 时空连续体
- 广义相对论
- 电梯内外
- 几何与实验
- 广义相对论及其验证
- 场与物质
III. Field, relativity
- The field as representation
- The two pillars of the field theory
- The reality of the field
- Field and ether
- The mechanical scaffold
- Ether and motion
- Time, distance, relativity
- Relativity and mechanics
- The time-space continuum
- General relativity
- Outside and inside the lift
- Geometry and experiment
- General relativity and its verification
- Field and matter
四、Quanta
- 连续性、不连续性
- 物质和电的基本量子
- 光的量子
- 光谱
- 物质波
- 概率波
- 物理与现实
IV. Quanta
- Continuity, discontinuity
- Elementary quanta of matter and electricity
- The quanta of light
- Light spectra
- The waves of matter
- Probability waves
- Physics and reality
指数
Index